Research Group in Global Analysis and Applications

http://globanal.upol.cz

Prof. RNDr. Olga Krupková, DrSc. photo

Positions:Head of Department of Mathematics, Faculty of Science, The University of Ostrava
Adjunct Professor, Faculty of Science, Technology and Engineering, La Trobe University, Melbourne (honorary position)
Professor, Faculty of Science, Palacký University, Olomouc (part time)
Addresses:Department of Mathematics
Faculty of Science, The University of Ostrava
30. dubna 22, 701 03 Ostrava, Czech Republic
&
Department of Mathematics and Statistics
Faculty of Science, Technology and Engineering
School of Engineering and Mathematical Sciences
La Trobe University, Bundoora, 3086 Victoria, Australia
Phone:+420 597 092 100
Fax:+420 596 120 478
E-mail:name@osu.cz, name@latrobe.edu.au
Homepage:http://globanal.upol.cz/krupkova.html
http://www.latrobe.edu.au/mathstats/staff/krupkova/index.html

List of citations


Olga Krupková (born Štěpánková), January 2010

The list contains 400 citations in books and monographs, research papers, and dissertations, of 45 articles.



O. Krupková, The Geometry of Ordinary Variational Equations, Lecture Notes in Mathematics 1678, Springer, Berlin, 1997.

Cited in:

  1. J. Novotný, Natural variational principles in physics, Textbook for the "3rd International Summer School on Global Analysis and Applications", Levoča, 1998 (Mathematical Institute Preprint Series GA 3/1998, Silesian University, Opava, 1998).
  2. R. Matsyuk, Hamilton-Ostrohradskyj approach to relativistic free spherical top dynamics, In: Proc. Conf. Diff. Geom. Appl., Brno 1998 (Masaryk Univ., Brno, 1999) 547-552.
  3. M. Mráz and J. Musilová, Variational compatibility of force laws, In: Proc. Conf. Diff. Geom. Appl., Brno 1998 (Masaryk Univ., Brno, 1999) 553-561.
  4. A. Vondra, From semisprays to connections, from geometry of regular O.D.E. in mechanics to geometry of horizontal Pfaffian P.D.E. on fibered manifolds (and vice versa), In: Proceedings of the Seminar on Differential Geometry, D. Krupka, ed., "Mathematical Publications" (Silesian University, Opava, Czechia, 2000).
  5. D. Krupka, J. Musilová, The variational sequence and trivial Lagrangians (in Czech), In: Proc. 13th Conf. of Slovak and Czech Physicists, Zvolen, 1999, M. Reiffers and L. Just, eds. (Technical University of Zvolen, Zvolen, Slovakia, 2000) 328-331.
  6. M. Mráz, J. Musilová, Non-parametrized Lagrange structures (in Czech), In: Proc. 13th Conf. of Slovak and Czech Physicists, Zvolen, 1999, M. Reiffers and L. Just, eds. (Technical University of Zvolen, Zvolen, Slovakia, 2000) 338-340.
  7. L. Klapka, Integrals and variational multipliers of second-order ordinary differential equations, Rend. Circ. Mat. Palermo Suppl. 63 (2000) 113-119.
  8. G. Sardanashvily, Classical and quantum mechanics with time-dependent parameters, J. Math. Phys. 41 (2000) 5245-5255.
  9. B. Deconinck, Canonical variables for multiphase solutions of the KP equation, Studies in Applied Math. 104 (2000) 229-292.
  10. L. Mangiarotti, G. Sardanashvily, On the geodesic form of second order dynamic equations, J. Math. Phys. 41 (2000) 835-844.
  11. J. Grifone, Z. Muzsnay, Variational Principles for Second-order Differential Equations, World Scientific, Singapore, 2000.
  12. D. Krupka, Global variational functionals on fibered spaces, Nonlinear Analysis 47 (2001) 2633-2642.
  13. D. Smetanová, On Hamilton p2-equations in second order field theory in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds. (Debrecen University, Debrecen, 2001) 329-341.
  14. D. Krupka, J. Musilová, Recent results in variational sequence theory, in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds. (Debrecen University, Debrecen, 2001) 161-186.
  15. P. Bracken, A differential geometric approach to the Helmholtz equations and an application to a space with a nontrivial Riemannian metric, Acta Appl. Math. 69 (2001) 129-139.
  16. R. Matsyuk, Autoparallel variational description of the free relativistic top third order dynamics, Proc. Conf. Diff. Geom. Appl., Opava, 2001 (Math. Publications, Vol. 3, Silesian Univ. Opava, 2001) 447-459.
  17. S. Martínez Díaz, Geometric methods in nonlinear control theory with applications to dynamic robotic systems, PhD Thesis, University Carlos III, Madrid, 2002, 268 pp.
  18. J. Janová, A geometric theory of mechanical systems with nonholonomic constraints (in Czech), Thesis, Masaryk University, Brno, 2002, 76 pp.
  19. S. Albeverio, A. Khrennikov, O. Smolyanov, A local Liouville theorem for infinite-dimensional Hamilton-Dirac systems, Rus. J. Math. Phys. 9 (2002) 123-139.
  20. D. Smetanová, The regularity problem in the calculus of variations, PhD Thesis, Palacký University, Olomouc, 2003.
  21. J. Cortés, M. De León, D.M. De Diego, S. Martinez, Geometric description of vakonomic and nonholonomic dynamics comparison of solutions, SIAM J. on Control and Optimization 41 (2003) 1389-1412.
  22. D.J. Saunders, Homogeneous Lagrangian systems, Rep. Math. Phys. 51 (2003) 315-324.
  23. J. Kotůlek, Z historie inverzního variačního problému: Odvození podmínek silné variačnosti, Pokroky matematiky, fyziky a astronomie 48 (2003) 222-238.
  24. R. Miron, The notion of higher order Finsler space. Theory and applications, In: Finslerian Geometries – a Meeting of Minds, Fundamental Theories of Physics 109 (Springer, Dordrecht, 2000) 193-208.
  25. D. Krupka, Global variational principles: Foundations and current problems, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 3-18.
  26. L. Czudková and J. Musilová, Variational non-holonomic systems in physics, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 131-140.
  27. M. Swaczyna, On the nonholonomic variational principle, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 297-306.
  28. M. de León, D.M. de Diego, A. Santamaria-Merino, Symmetries in classical field theory, Int. J. Geom. Met. Mod. Phys. 1 (2004) 651-710.
  29. D. Baleanu, About fractional calculus of singular Lagrangians, In: ICCC 2004: Second IEEE International Conference on Computational Cybernetics, Proceedings, Vienna Univ. Technol, Vienna, 2004 (IEEE, New York, USA, 2004) 379-384.
  30. J. Šeděnková, Representations of variational sequences and Lepage forms, PhD Thesis, Palacký University, Olomouc, 2004.
  31. L. Czudková, J. Janová and J. Musilová, Non-holonomic mechanical systems and variational principle, In: Differential Geometry and its Applications, Proc. Conf. Prague 2004 (Charles University, Prague, 2005) 571-579.
  32. R. Matsyuk, Canonical formalism for quasi-classical particle "Zitterbewegung" in Ostrohradskyj mechanics, in: Differential Geometry and its Applications, Proc. Conf. Prague 2004 (Charles University, Prague, 2005) 629-637.
  33. M. Swaczyna, Variational Aspects of Nonholonomic Mechanical Systems, PhD Thesis, Palacký University, Olomouc, 2005, 121 pp.
  34. J. Brajerčík, D. Krupka, Variational principles for locally variational forms, J. Math. Phys. 46 (2005) 052903.
  35. R. Benito, D.M. de Diego, Discrete vakonomic mechanics, J. Math. Phys. 46 (2005) 083521.
  36. M. Krbek, J. Musilová, Representation of the variational sequence by differential forms, Acta Appl. Math. 88 (2005) 177-199.
  37. X. Gracia, R. Martin, Geometric aspects of time-dependent singular differential equations, Int. J. Geom. Met. Mod. Phys. 2 (2005) 597-618.
  38. I. Bucataru, Linear connections for systems of higher order differential equations, Houston J. Math. 31 (2005) 315-332.
  39. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.
  40. L. Czudková, J. Janová, J. Musilová, Trivial constraint variational problem, Rend. Circ. Mat. Palermo, Serie II, Suppl. 79 (2006) 67-74.
  41. J. Janová, Mechanics of nonholonomic constrainned systems, PhD Thesis, Masaryk University, Brno, 2006.
  42. I. Bucataru and R. Miron, Finsler-Lagrange Geometry: Applications to Dynamical Systems (Editura Academiei Romane, Bucuresti, 2007) ISBN 978-973-27-1527-7.
  43. P. Morando, Variational lambda-symmetries and deformed Lie derivative, In: Symmetry and Perturbation Theory, Proc. Int. Conf. SPT 2007, Otranto, G. Gaeta, R. Vitolo and S. Walcher (Eds.), World Scientific, Singapore, 2007, 140-147.
  44. F. Cantrijn and J. Vankerschaver, The Skinner-Rusk approach for vakonomic and nonholonomic field theories, In: Differential Geometric Methods in Mechanics and Field Theory (Academia Press, Gent, 2007) 1-13.
  45. D. Krupka, The structure of the Euler-Lagrange mapping, paper in honour of N.I. Lobachevskii, Russian Mathematics (Iz. VUZ) 51 (12) (2007), N.I. Lobachevskii Anniversary Volume, 52-70.
  46. D. Smetanová, J. Volná, P. Volný, Variational principles on fibred manifolds, Proceedings of the Workshop "Matematika na vysokých školách" (Union of Czech Mathematicians and Physicists & Technical University in Prague, Prague, 2007) 109-112, ISBN 978-80-01-03773-7.
  47. I. Bucataru, R. Miron, Nonlinear connections for nonconservative mechanical systems, Rep. Math. Phys. 59 (2007) 225-241.
  48. P. Morando, Deformation of Lie derivative and mu-symmetries, J. Phys. A: Mat. Theor. 40 (2007) 11547-11559.
  49. I. Bucataru, Metric nonlinear connections, Diff. Geom. Appl. 25 (2007) 335-343.
  50. R. Ya. Matsyuk, The Variational Principle for the Uniform Acceleration and Quasi-Spin in Two Dimensional Space-Time, Symmetry, Integrability and Geometry: Methods and Applications SIGMA 4 (2008), 016, 11 pp.
  51. J. Musilová and M. Lenc, Lepage forms in variational theories: From Lepage’s idea to the variational sequence, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 3-27.
  52. D.R. Grigore, On a generalization of the Poincaré-Cartan form in higher-order field theory, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 55-76
  53. L. Czudková and J. Musilová, Non-holonomic constraint forces in field theory in physics, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 603-613.
  54. M. Swaczyna, Constraint Lepage one forms in higher order mechanics with nonholonomic constraints on the dynamical space, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 689-702.
  55. J. Korbaš, Distributions, vector distributions, and immersions of manifolds in Euclidean spaces, In: Handbook of Global Analysis (Elsevier, 2008) 665-724.
  56. D. Krupka, Global variational theory in fibred spaces, In: Handbook of Global Analysis (Elsevier, 2008) 773-836.
  57. R. Vitolo, Variational sequences, In: Handbook of Global Analysis (Elsevier, 2008) 1115-1163.
  58. D. Baleanu, Nonconservative systems within fractional generalized derivatives, J. Vibration and Control 14 (2008) 1301-1311.
  59. J. Janová and J. Musilová, Non-holonomic mechanics: A geometrical treatment of general coupled rolling motion, Int. J. Non-Linear Mechanics 44 (2009) 98-105.
  60. R. Matsyuk, Invariant variational equations of the third order in planar special relativity (in Ukrainian), Праці Міжнародного геометричного центру (Nauka, Lviv), to be published.
  61. M. Lenc, J. Musilová and L. Czudková, Lepage forms theory applied, Arch. Math. (Brno), to be published.
  62. I. Bucataru and M.F. Dahl, Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations, J. Geom. Mech. 1 (2009) 159-180.
  63. M. Lenc, J. Musilová and L. Czudková, Lepage forms theory applied, Arch. Math. (Brno) 45 (2009) 279-287.
  64. R. Malíková, On a generalization of Helmholtz conditions, Acta Math. Univ. Ostraviensis 17 (2009) 11-21.
  65. D. Krupka and Z. Urban, Variational sequences in mechanics on Grassmann fibrations, Acta Appl. Math., to be published.
  66. I. Bucataru and R. Miron, The geometry of systems of third order differential equations induced by second order regular Lagrangians, Mediterranean J. Math. 6 (4) (2009) 483-500.

O. Krupková, Lepagean 2-forms in higher order Hamiltonian mechanics, I. Regularity, Arch. Math. (Brno) 22 (1986) 97-120.

Cited in:

  1. D. Krupka, In: Differential Geometry and Its Applications, Proc. Conf., Brno, Czechoslovakia, 1986 (D. Reidel, Dordrecht, 1986) 111-148.
  2. A. Vondra, In: Differential Geometry and Its Applications, Proc. Conf., Brno, Czechoslovakia, 1989, J. Janyška and D. Krupka eds. (World Scientific, Singapore, 1990), 276-287.
  3. A. Vondra, Connections in the geometry of non-autonomous regular higher-order dynamics, PhD Thesis (Dept. of Algebra and Geometry, Masaryk Univ., Brno, Czechoslovakia, 1991) 42 pp.
  4. A. Vondra, On some connections related to the geometry of regular higher-order dynamics, Sborník VA Brno, Řada B2/1992, 7-18.
  5. D. J. Saunders, The regularity of variational problems, In: Mathematical Aspects of Classical Field Theory, Proc. of the AMS-IMS-SIAM Conf. 1991, M. J. Gotay, J. E. Marsden and V. Moncrief, eds., Contemporary Math. 132 (Amer. Math. Soc., 1992) 573-593
  6. A. Dekrét, Natural operations with connections, DrSc. Dissertation, University of Košice, 1992.
  7. V.M. Filipov, V.M. Savčin, S.G. Šorochov, Variational principles for nonpotential operators (Itogi nauki i techniki, Sovremennye problemy matematiki 40, VINITI, Moscow 1992) (in Russian).
  8. P. J. Olver, Equivalence and the Cartan form, Acta Appl. Math. 31 (1993) 99-136.
  9. D. R. Grigore, Higher order Lagrangian theories and Noetherian symmetries, Roum. J. Phys. 39 (1994) 11-35.
  10. D. Krupka, Lectures on Variational Sequences (Open Education & Sciences, Opava, 1995) 94 pp.
  11. A. Vondra, Towards a Geometry of Higher-Order Partial Differential Equations Represented by Connections on Fibered Manifolds, Habilitation Thesis, Masaryk University Brno, 1995, 114 pp.
  12. M. de León, J. Marín-Solano and J. C. Marrero, The constraint algorithm in the jet formalism, Diff. Geom. Appl., 6 (1996) 275-299.
  13. A. Vondra, Prolongations and fields of paths for higher-order O.D.E. represented by connections on a fibered manifold, Extracta Mathematicae 11 (1996) 229-24.
  14. D. R. Grigore, On an order reduction theorem in the Lagrangian formalism, Nuovo Cimento B 111 (1996) 1439-1447.
  15. D. Krupka, Variational sequences in mechanics, Calculus of Variations 5 (1997) 557-583.
  16. R. Matsyuk, Third-order relativistic dynamics: classical spinning particle travelling in a plane, Condensed Matter Physics 1, No. 3 (15) (1998).
  17. A Vondra, Higher-order differential equations represented by connections on prolongations of a fibered manifold, Extracta Mathematicae 15 (3) (2000) 421-512.
  18. A. Vondra, From semisprays to connections, from geometry of regular O.D.E. in mechanics to geometry of horizontal Pfaffian P.D.E. on fibered manifolds (and vice versa), In: Proceedings of the Seminar on Differential Geometry, D. Krupka, ed., "Mathematical Publications" (Silesian University, Opava, Czechia, 2000).
  19. D. Krupka, Global variational functionals on fibered spaces, Nonlinear Analysis 47 (2001) 2633-2642.
  20. D. Krupka, J. Musilová, Recent results in variational sequence theory, in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds. (Debrecen University, Debrecen, 2001) 161-186.
  21. D.J. Saunders, On the inverse problem for even-order ordinary differential equations in the higher-order calculus of variations, Diff. Geom. Appl. 16 (2002) 149-166.
  22. M. de León, J. Martín-Solano, J.C. Marrero, Singular Lagrangian systems on jet bundles, Fortschr. Phys. 50 (2002) 105-169.
  23. D. Krupka, Global variational principles: Foundations and current problems, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 3-18.
  24. J. Šeděnková, Representations of variational sequences and Lepage forms, PhD Thesis, Palacký University, Olomouc 2004.
  25. J. Šeděnková, A generalization of Lepage forms in mechanics, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 281-288.
  26. D. Krupka and J. Šeděnková, Variational sequences and Lepage forms, in: Differential Geometry and its Applications, Proc. Conf. Prague 2004 (Charles University, Prague, 2005) 617-627.
  27. J. Brajerčík, D. Krupka, Variational principles for locally variational forms, J. Math. Phys. 46 (2005) 052903.
  28. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.
  29. D. Krupka, The Vainberg-Tonti Lagrangian and the Euler-Lagrange mapping, in: Differential Geometric Methods in Mechanics and Field Theory (Academia Press, Gent, 2007) 81-90.
  30. D. Krupka, The structure of the Euler-Lagrange mapping, paper in honour of N.I. Lobachevskii, Russian Mathematics (Iz. VUZ) 51 (12) (2007), N.I. Lobachevskii Anniversary Volume, 52-70.
  31. J. Musilová and M. Lenc, Lepage forms in variational theories: From Lepage’s idea to the variational sequence, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 3-27.
  32. D.R. Grigore, On a generalization of the Poincaré-Cartan form in higher-order field theory, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 55-76.
  33. D. Krupka, Global variational theory in fibred spaces, In: Handbook of Global Analysis (Elsevier, 2008) 773-836.
  34. R. Malíková, On a generalization of Helmholtz conditions, Acta Math. Univ. Ostraviensis 17 (2009) 11-21.

O. Krupková, Mechanical systems with non-holonomic constraints, J. Math. Phys. 38 (1997) 5098-5126.

Cited in:

  1. A. Ibort, M. de León, E. A. Lacomba, J. C. Marrero, D. Martín de Diego, P. Pitanga, Geometric formulation of mechanical systems subjected to time-dependent one-sided constraints, J. Phys. A: Math. Gen. 31 (1998) 2655-2674.
  2. D.J. Saunders, The geometry of non-holonomic Lagrangian systems, Proc. Conf. Diff. Geom. Appl., Brno 1998 (Masaryk Univ., Brno, 1999) 575-579.
  3. A. Ibort, M. de León, J.C. Marrero and D.M. de Diego, Dirac brackets in constrained dynamics, Fortschr. Phys. 47 (1999) 459-492.
  4. G. Giachetta, L. Mangiarotti, G. Sardanashvily, Nonholonomic constraints in time-dependent mechanics, J. Math. Phys. 40 (1999) 1376-1390.
  5. M. de León, J.C. Marrero, D.M. de Diego, Vakonomic mechanics versus non-holonomic mechanics: a unified geometrical approach, J. Math. Phys. 35 (2000) 126-144.
  6. J. Cortés Monforte, Geometric, control and numetric aspects of nonholonomic systems, PhD Thesis, University Carlos III, Madrid, 2001, 221 pp.
  7. F. Cantrijn, J. Cortés and M. de León, On the geometry of generalized Chaplygin systems, Math. Proc. Cambridge 132 (2002) 323-351.
  8. J. Janová, A geometric theory of mechanical systems with noholonomic constraints (in Czech), Thesis, Masaryk University, Brno, 2002, 76 pp.
  9. J. Cortés Monforte, Geometric, Control and Numerical Aspects of Nonholonomic Systems, LNM 1793, Springer, Berlin, 2002.
  10. F. Cantrijn, J. Cortes, Cosymplectic reduction of constrained systems with symmetry, Reports on Math. Phys. 49 (2002) 167-182.
  11. L. Czudková and J. Musilová, Variational non-holonomic systems in physics, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 131-140.
  12. M. Swaczyna, On the nonholonomic variational principle, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 297-306.
  13. D. Baleanu, About fractional calculus of singular Lagrangians, In: ICCC 2004: Second IEEE International Conference on Computational Cybernetics, Proceedings, Vienna Univ Technol, Vienna, 2004 (IEEE, New York, USA, 2004) 379-384.
  14. W. Sarlet, Adjoint symmetries in non-holonomic mechanics, In: Differential Geometry and its Applications, Proc. Conf. Prague 2004 (Charles University, Prague, 2005) 537-548.
  15. L. Czudková, J. Janová and J. Musilová, Non-holonomic mechanical systems and variational principle, in: Differential Geometry and its Applications, Proc. Conf. Prague 2004 (Charles University, Prague, 2005) 571-579.
  16. M. Swaczyna, Variational Aspects of Nonholonomic Mechanical Systems, PhD Thesis, Palacký University, Olomouc, 2005, 121 pp.
  17. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.
  18. L. Czudková, J. Janová, J. Musilová, Trivial constraint variational problem, Rend. Circ. Mat. Palermo, Serie II, Suppl. 79 (2006) 67-74.
  19. J. Janová, Mechanics of nonholonomic constrainned systems, PhD Thesis, Masaryk University, Brno, 2006.
  20. J. Musilová and M. Lenc, Lepage forms in variational theories: From Lepage’s idea to the variational sequence, In: Variations, Geometry and Physics, Volume in honour of D. Krupka's 65th birthday (Nova Science Publishers, New York, 2008) 3-27.
  21. L. Czudková and J. Musilová, Non-holonomic constraint forces in field theory in physics, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 603-613.
  22. M. Swaczyna, Constraint Lepage one forms in higher order mechanics with nonholonomic constraints on the dynamical space, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 689-702.
  23. A. Kundu, Exact accelerating solitons in nonholonomic deformation of the KdV equation with a two-fold integrable hierarchy, J. Phys. A: Math. Theor. 41 (2008) 495201.
  24. C. Liu, S.X. Liu, F.X. Mei, Y.X. Guo, Conformal invariance and Hojman conserved quantities of generalized Hamilton systems, Acta Physica Sinica 57 (2008) 6709-6713.
  25. J. Janová and J. Musilová, Non-holonomic mechanics: A geometrical treatment of general coupled rolling motion, Int. J. Non-Linear Mechanics 44 (2009) 98-105.
  26. M. Lenc, J. Musilová and L. Czudková, Lepage forms theory applied, Arch. Math. (Brno) 45 (2009) 279-287.
  27. J. Janová, J. Musilová and J. Bartoš, Coupled rolling motion: a student project in non-holonomic mechanics, Eur. J. Phys. 30 (2009) 1257–1269.
  28. X.W. Chen, Conformal invariance and conserved quantity for holonomic mechanical systems with variable mass, Acta Physica Sinica 58 (8) (2009) 5150.

O. Krupková, Variational Analysis on Fibered Manifolds over One-dimensional Bases, PhD Thesis, Silesian University, Opava & Charles University, Prague, 1992.

Cited in:

  1. M. de León, J. C. Marrero, Degenerate time-dependent Lagrangians of second order: the fourth order differential equation problem, In: Proc. Conf. on Diff. Geom and Its Appl., (Silesian University, Opava, 1992) 497- 508.
  2. A Dekrét, Natural operations with connections (in Slovak), DrSc. Dissertation, University of Košice, 1992.
  3. D. Chinea, M. de León and J. C. Marrero, The constraint algorithm for time-dependent Lagrangians, J. Math. Phys. 35 (1994) 3410-3447.
  4. J. Debecki, J. Gancarzewicz, M. de León and W. Mikulski, Invariants of Lagrangians and their classifications, J. Math. Phys. 35 (1994) 4568-4593.
  5. A. Vondra, Symmetries of connections on fibered manifolds, Arch. Math. (Brno), 30 (1994) 97-115.
  6. Z. Oziewicz, Classical field theory and analogy between Newton's and Maxwell's equations, Found. Phys. 24 (1994) 1379-1402.
  7. M. Gusiew-Czudzak and Z. Oziewicz, Poincaré-Cartan subbundles, Proc. XXIIth Int. Conf. on Diff. Geom. Methods in Theor. Phys., Ixtapa-Zihuatanejo, México, 1993, J. Keller and Z. Oziewicz, eds. (Univ. Nacional Autónoma de México, 1994) 325-339.
  8. D. R. Grigore, Higher order Lagrangian theories and Noetherian symmetries, Roum. J. Phys. 39 (1994) 11-35.
  9. D. Krupka, Lectures on Variational Sequences. (Open Education & Sciences, Opava, 1995) 94 pp.
  10. A. Vondra, Geometry of second-order connections and ordinary differential equations, Math. Bohemica 120 (1995) 145-167.
  11. R. Miron, Noether theorem in the higher order Lagrangian mechanics, Int. J. Theor. Phys. 34 (1995) 1123-1146.
  12. D. R. Grigore, Variational equations and symmetries in the Lagrangian formalism, J. Phys. A: Math. Gen., 28 (1995) 2921-2937.
  13. A. Vondra, Towards a Geometry of Higher-Order Partial Differential Equations Represented by Connections on Fibered Manifolds, Habilitation Thesis, Masaryk University, Brno, 1995, 114 pp.
  14. A. Vondra, Prolongations and fields of paths for higher-order O.D.E. represented by connections on a fibered manifold, Extracta Mathematicae 11 (1996) 229-24.
  15. M. de León, J. Marín-Solano and J. C. Marrero, The constraint algorithm in the jet formalism, Diff. Geom. Appl., 6 (1996) 275-299.
  16. R. Miron, The Geometry of Higher-Order Lagrange Spaces: Applications to Mechanics and Physics, Kluwer, 1997.
  17. D. Krupka, Variational sequences in mechanics, Calculus of Variations 5 (1997) 557-583.
  18. J. Lopuszanski, P. C. Stichel, Most general form of the Lagrange function for classical 2 particle equation of motion covariant under Galilei transformation in (1+1)-dimensional spaces and (3+1)-dimensional spaces, Fortschritte der Physik 45 (1997) 79-97.
  19. A. Vondra, Higher-order differential equations represented by connections on prolongations of a fibered manifold, Extracta Mathematicae 15 (3) (2000) 421-512.
  20. A. Vondra, From semisprays to connections, from geometry of regular O.D.E. in mechanics to geometry of horizontal Pfaffian P.D.E. on fibered manifolds (and vice versa), In: Proceedings of the Seminar on Differential Geometry, D. Krupka, ed., "Mathematical Publications" (Silesian University, Opava, Czechia, 2000).
  21. D. Krupka, J. Musilová, Recent results in variational sequence theory, in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds.(Debrecen University, Debrecen, 2001) 161-186.
  22. J. Šeděnková, Representations of variational sequences and Lepage forms, PhD Thesis, Palacký University, Olomouc, 2004.
  23. J. Musilová and M. Lenc, Lepage forms in variational theories: From Lepage’s idea to the variational sequence, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 3-27.
  24. D.R. Grigore, On a generalization of the Poincaré-Cartan form in higher-order field theory, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 55-76.

D. Krupka and O. Štěpánková, On the Hamilton form in second order calculus of variations, In: Proc. Internat. Meeting "Geometry and Physics", Florence 1982, (Pitagora Bologna, 1983) 85-101.

Cited in:

  1. P. L. García and J. M. Masqué, C. R. Acad. Sci. Paris 301, Sér. I (1985) 639-642.
  2. D. Krupka, in: Differential Geometry and Its Applications, Proc. Conf., Brno, Czechoslovakia, 1986 (D. Reidel, Dordrecht, 1986) 111-148.
  3. V. Sczyrba, Phys. Rev. D 36 (1987) 351-374.
  4. P.J. Olver, Equivalence and the Cartan form, Acta Appl. Math. 31 (1993) 99-136.
  5. M. de León, J. Marín-Solano and J. C. Marrero, The constraint algorithm in the jet formalism, Diff. Geom. Appl., 6 (1996) 275-299.
  6. G. Giachetta, G. Sardanashvily, Energy-momentum superpotential in gravitation theory, in: Gravity, Particles and Space-time (World Scientific, Singapore, 1996) 471-506.
  7. G.A. Sardanashvily, Stress-energy-momentum tensors in constraint field theories, J. Math. Phys. 38 (1997) 847-866.
  8. G. Giachetta, L. Mangiarotti and G. Sardanashvily, New Lagrangian and Hamiltonian Methods in Field Theory, World Scientific, Singapore, 1997.
  9. I. V. Kanatchikov, Precanonical perspective in quantum gravity, Nucl. Phys. B-Proc. Sup. 88 (2000) 326-330.
  10. D. Krupka, Global variational functionals on fibered spaces, Nonlinear Analysis 47 (2001) 2633-2642.
  11. D. Smetanová, On Hamilton p2-equations in second order field theory in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds.(Debrecen University, Debrecen, 2001) 329-341.
  12. D. Krupka, J. Musilová, Recent results in variational sequence theory, in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds.(Debrecen University, Debrecen, 2001) 161-186.
  13. M. J. Gotay, J. A. Isenberg, J. E. Marsden and R. Montgomery, Momentum Mappings and the Hamiltonian Structure of Classical Field Theories with Constraints, M.S.R.I. Publications, Springer, New York, 2001.
  14. M. de León, J. Martín-Solano, J.C. Marrero, Singular Lagrangian systems on jet bundles, Fortschr. Phys. 50 (2002) 105-169.
  15. D. Smetanová, The regularity problem in the calculus of variations, PhD Thesis, Palacký University, Olomouc, 2003.
  16. D. Krupka, Global variational principles: Foundations and current problems, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 3-18.
  17. D. Smetanová, On regularization of second order Lagrangians, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 289-296.
  18. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.
  19. D. Krupka, The structure of the Euler-Lagrange mapping, paper in honour of N.I. Lobachevskii, Russian Mathematics (Iz. VUZ) 51 (12) (2007), N.I. Lobachevskii Anniversary Volume, 52-70.
  20. D. Smetanová, J. Volná, P. Volný, Variational principles on fibred manifolds (in Czech), In: Proceedings of the Workshop "Matematika na vysokých školách" (Union on Czech Mathematicians and Physicists & Technical University in Prague, Prague, 2007) 109-112, ISBN 978-80-01-03773-7.
  21. A. Fernández and P.L. García, Lepage congruences in discrete mechanics, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 85-97.
  22. D. Krupka, Global variational theory in fibred spaces, In: Handbook of Global Analysis (Elsevier, 2008) 773-836.
  23. M.J. Gotay and J.E. Marsden, Momentum Maps and Classical Fields, Lecture Notes, 14th Int. Summer School on Glob. Anal. and Math. Phys., Olomouc, 2009, Satellite Conf. of XVI Int. Congress on Math. Phys., Prague, 2009, 271 pp.

O. Krupková, Lepagean 2-forms in higher order Hamiltonian mechanics, II. Inverse problem, Arch. Math. (Brno) 23 (1987) 155-170.

Cited in:

  1. A. Vondra, in: Differential Geometry and Its Applications, Proc. Conf., Brno, Czechoslovakia, 1989, J. Janyäka and D. Krupka eds. (World Scientific, Singapore, 1990), 276-287.
  2. A. Vondra, Connections in the geometry of non-autonomous regular higher-order dynamics, PhD Thesis, Masaryk University, Brno, 1991, 42 pp.
  3. A. Vondra, On some connections related to the geometry of regular higher-order dynamics, Sborník VA Brno, Řada B2/1992, 7-18.
  4. D. Krupka, Lectures on Variational Sequences. Mechanics, Open Education & Sciences, Opava, 1995, 94 pp.
  5. A. Vondra, Towards a Geometry of Higher-Order Partial Differential Equations Represented by Connections on Fibered Manifolds, Habilitation Thesis, Masaryk University, Brno, 1995, 114 pp.
  6. M. de León, J. Marín-Solano and J. C. Marrero, The constraint algorithm in the jet formalism, Diff. Geom. Appl., 6 (1996) 275-299.
  7. A. Vondra, Prolongations and fields of paths for higher-order O.D.E. represented by connections on a fibered manifold, Extracta Mathematicae 11 (1996) 229-24.
  8. D. Krupka, Variational sequences in mechanics, Calculus of Variations 5 (1997) 557-583.
  9. A. Vondra, Higher-order differential equations represented by connections on prolongations of a fibered manifold, Extracta Mathematicae 15 (3) (2000) 421-512.
  10. A. Vondra, From semisprays to connections, from geometry of regular O.D.E. in mechanics to geometry of horizontal Pfaffian P.D.E. on fibered manifolds (and vice versa), In: Proceedings of the Seminar on Differential Geometry, D. Krupka, ed., "Mathematical Publications" (Silesian University, Opava, Czechia, 2000).
  11. D. Krupka, Global variational functionals on fibered spaces, Nonlinear Analysis 47 (2001) 2633-2642.
  12. D. Krupka, J. Musilová, Recent results in variational sequence theory, in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds. (Debrecen University, Debrecen, 2001) 161-186.
  13. M. de León, J. Martín-Solano, J.C. Marrero, Singular Lagrangian systems on jet bundles, Fortschr. Phys. 50 (2002) 105-169.
  14. D. Krupka, Global variational principles: Foundations and current problems, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 3-18.
  15. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.
  16. D. Krupka, The Vainberg-Tonti Lagrangian and the Euler-Lagrange mapping, in: Differential Geometric Methods in Mechanics and Field Theory (Academia Press, Gent, 2007) 81-90.
  17. J. Musilová and M. Lenc, Lepage forms in variational theories: From Lepage’s idea to the variational sequence, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 3-27.
  18. D.R. Grigore, On a generalization of the Poincaré-Cartan form in higher-order field theory, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 55-76.
  19. D. Krupka, Global variational theory in fibred spaces, In: Handbook of Global Analysis (Elsevier, 2008) 773-836.

O. Krupková, Hamiltonian field theory, J. Geom. Phys. 43 (2002) 93-132.

Cited in:

  1. D. Smetanová, On Hamilton p2-equations in second order field theory in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds.(Debrecen University, Debrecen, 2001) 329-341.
  2. M. Francaviglia, M. Palese, E. Winterroth, A new geometric proposal for the Hamiltonian description of classical field theories, Proc. Conf. Diff. Geom. Appl., Opava, 2001 (Math. Publications, Vol. 3, Silesian Univ. Opava, 2001) 415-423.
  3. I. Kanatchikov, Geometric (pre)quantization in the polysymplectic approach to field theory, Proc. Conf. Diff. Geom. Appl., Opava (Math. Publications, Vol. 3, Silesian Univ. Opava, 2001) 309-321.
  4. J.B. Chen, Multisymplectic geometry, local conservation laws and a multisymplectic integrator for the Zakharov-Kuznetsov equation, Letters in Math. Phys. 63 (2003) 115-124.
  5. D. Krupka, Global variational principles: Foundations and current problems, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 3-18.
  6. D. Smetanová, On regularization of second order Lagrangians, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 289-296.
  7. M. de León, D.M. de Diego, A. Santamaria-Merino, Symmetries in classical field theory, Int. J. Geom. Met. Mod. Phys. 1 (2004) 651-710.
  8. X. Gracia, M.C. Munoz-Lecanda, N. Roman-Roy, On some aspects of the geometry of differential equations in physics, Int. J. Geom. Met. Mod. Phys. 1 (2004) 265-284.
  9. M. Francaviglia, M. Palese, E. Winterroth, A general geometric setting for the energy of the gravitational field, In: Recent developments in gravitational physics, IOP Conf. Series, 176, Taylor & Francis, 2006, 391-395.
  10. M. Palese, E. Winterroth, Some aspects of the homogeneous formalism in field theory and gauge invariance, Arch. Math. (Brno) 42 (2006) Suppl., 319-327.
  11. D. Krupka, The structure of the Euler-Lagrange mapping, paper in honour of N.I. Lobachevskii, Russian Mathematics (Iz. VUZ) 51 (12) (2007), N.I. Lobachevskii Anniversary Volume, 52-70
  12. D.R. Grigore, On a generalization of the Poincaré-Cartan form in higher-order field theory, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 55-76.
  13. M. Castrillón López and J. Munoz-Masqué, Lie algebra pairing and the Lagrangian and Hamiltonian equations in gauge-invariant problems, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 595-602.
  14. I. Kanatchikov, On a generalization of the Dirac bracket in the De-Donder-Weyl Hamiltonian formalism, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 615-625.
  15. D. Krupka, Global variational theory in fibred spaces, In: Handbook of Global Analysis (Elsevier, 2008) 773-836.
  16. M. Crampin and D.J. Saunders, Some concepts of regularity for parametric multiple-integral problems in the calculus of variations, Czechoslovak Math. J. 59 (3) (2009) 741-758.
  17. N. Román-Roy, Multisymplectic Lagrangian and Hamiltonian formalisms of classical field theories, Symmetry, Integrability and Geometry – Methods and Applications (SIGMA) 5 Art. No. 100 (2009), 25pp.

O. Krupková, A geometric setting for higher-order Dirac-Bergmann theory of constraints, J. Math. Phys. 35 (1994) 6557-6576.

Cited in:

  1. D. Krupka, Lectures on Variational Sequences. Mechanics (Open Education & Sciences, Opava, 1995) 94 pp.
  2. M. de León, D. Martín de Diego and P. Pitanga, A new look at degenerate Lagrangian dynamics from the viewpoint of almost product structures, J. Phys. A: Math. Gen. 28 (1995) 4951-4971.
  3. M. de León, J. Marín-Solano and J. C. Marrero, The constraint algorithm in the jet formalism, Diff. Geom. Appl., 6 (1996) 275-299.
  4. M. de León and D. Martín de Diego, Symmetries and constants of the motion for singular Lagrangian systems, Int. J. Theor. Phys. 35 (1996) 975-1011.
  5. D. Krupka, Variational sequences in mechanics, Calculus of Variations 5 (1997) 557-583.
  6. Y. Yaremko, Contact transformations in Wheeler-Feynman electrodynamics, Annals Inst. Poincaré, Physique Theorique 66 (1997) 293-322.
  7. R. Matsyuk, Third-order relativistic dynamics: classical spinning particle travelling in a plane, Condensed Matter Physics 1, No. 3 (15) (1998).
  8. D. Krupka, Global variational functionals on fibered spaces, Nonlinear Analysis 47 (2001) 2633-2642.
  9. D. Krupka, J. Musilová, Recent results in variational sequence theory, in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds. (Debrecen University, Debrecen, 2001) 161-186.
  10. M. de León, J. Martín-Solano, J.C. Marrero, Singular Lagrangian systems on jet bundles, Fortschr. Phys. 50 (2002) 105-169.
  11. D. Krupka, Global variational principles: Foundations and current problems, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 3-18.

O. Krupková, Higher order mechanical systems with constraints, J. Math. Phys. 41 (2000) 5304-5324.

Cited in:

  1. R. Matsyuk, A covering second-order Lagrangian for the relativistic top without forces, Proc. Inst. Math. of NAS of Ukraine 43 (2002) 741-745.
  2. J. Cortés Monforte, Geometric, Control and Numerical Aspects of Nonholonomic Systems, LNM 1793, Springer, Berlin, 2002.
  3. H. Cendra, A. Ibort, M. de León, D.M. de Diego, A generalization of Chetaev's principle for a class of higher order nonholonomic constraints, J. Math. Phys. 45 (2004) 2785-2801.
  4. M. Swaczyna, Variational Aspects of Nonholonomic Mechanical Systems, PhD Thesis, Palacký University, Olomouc, 2005, 121 pp.
  5. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.
  6. H. Cendra, S. Grillo, Generalized nonholonomic mechanics, servomechanisms and related brackets, J. Math. Phys. 47 (2006) 022902.
  7. J. Janová, Mechanics of nonholonomic constrainned systems, PhD Thesis, Masaryk University, Brno, 2006.
  8. H. Cendra H, S.D. Grillo, Lagrangian systems with higher order constraints, J. Math. Phys. 48 (2007) 052904.
  9. M. Swaczyna, Constraint Lepage one forms in higher order mechanics with nonholonomic constraints on the dynamical space, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 689-702.
  10. S.I. Vacaru, Finsler and Lagrange geometries in Einstein and string gravity, Int. J. Geom. Met. Mod. Phys. 5 (2008) 473-511.
  11. J. Janová and J. Musilová, Non-holonomic mechanics: A geometrical treatment of general coupled rolling motion, Int. J. Non-Linear Mechanics 44 (2009) 98-105.

O. Krupková, Hamiltonian field theory revisited: A geometric approach to regularity, in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds. (Debrecen University, Debrecen, 2001) 187-207.

Cited in:

  1. D. Smetanová, On Hamilton p2-equations in second order field theory in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds. (Debrecen University, Debrecen, 2001) 329-341.
  2. D. Krupka, J. Musilová, Recent results in variational sequence theory, in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds. (Debrecen University, Debrecen, 2001) 161-186.
  3. D. Smetanová, The regularity problem in the calculus of variations, PhD Thesis, Univerzita Palackého, Olomouc, 2003.
  4. D. Krupka, Global variational principles: Foundations and current problems, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 3-18.
  5. J. Šeděnková, A generalization of Lepage forms in mechanics, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 281-288.
  6. D. Smetanová, On regularization of second order Lagrangians, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 289-296.
  7. D. Krupka and J. Šeděnková, Variational sequences and Lepage forms, in: Differential Geometry and its Applications, Proc. Conf. Prague 2004 (Charles University, Prague, 2005) 617-627.
  8. J. Šeděnková, Representations of variational sequences and Lepage forms, PhD Thesis, Palacký University, Olomouc, 2004.
  9. D. Krupka, The Vainberg-Tonti Lagrangian and the Euler-Lagrange mapping, in: Differential Geometric Methods in Mechanics and Field Theory (Academia Press, Gent, 2007) 81-90.
  10. D.R. Grigore, On a generalization of the Poincaré-Cartan form in higher-order field theory, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 55-76.
  11. D. Krupka, Global variational theory in fibred spaces, In: Handbook of Global Analysis (Elsevier, 2008) 773-836.

O. Krupková and J. Musilová, The relativistic particle as a mechanical system with non-holonomic constraints, J. Phys. A: Math. Gen. 34 (2001) 3859-3875.

Cited in:

  1. J. Janová, A geometric theory of mechanical systems with nonholonomic constraints (in Czech), Thesis, Masaryk University, Brno, 2002, 76 pp.
  2. Z.X. Xu, Y.X. Guo and W. Wu, A connection theory for a nonlinear differential constrained system, Chinese Physics 11 (12) (2002) 1228-1233.
  3. L. Czudková and J. Musilová, Variational non-holonomic systems in physics, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 131-140.
  4. L. Czudková, J. Janová and J. Musilová, Non-holonomic mechanical systems and variational principle, in: Differential Geometry and its Applications, Proc. Conf. Prague 2004 (Charles University, Prague, 2005) 571-579.
  5. X. Grácia and R. Martín, Regularity and symmetries of nonholonomic systems, J. Phys. A: Math. Gen. 38 (2005) 1071-1087.
  6. M. Swaczyna, Variational Aspects of Nonholonomic Mechanical Systems, PhD Thesis, Palacký University, Olomouc, 2005, 121 pp.
  7. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.
  8. J. Janová, Mechanics of nonholonomic constrainned systems, PhD Thesis, Masaryk University, Brno, 2006.
  9. J. Janová and J. Musilová, Non-holonomic mechanics: A geometrical treatment of general coupled rolling motion, Int. J. Non-Linear Mechanics 44 (2009) 98-105.
  10. M. Lenc, J. Musilová and L. Czudková, Lepage forms theory applied, Arch. Math. (Brno) 45 (2009) 279-287.
  11. V.E. Tarasov, Fractional Dynamics of Relativistic Particle, Int. J. Theor. Phys. 49 (2) (2010) 293-303.

O. Krupková and D. Smetanová, Legendre transformation for regularizable Lagrangians in field theory, Letters in Math. Phys. 58 (2001) 189-204.

Cited in:

  1. D. Smetanová, On Hamilton p2-equations in second order field theory in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds. (Debrecen University, Debrecen, 2001) 329-341.
  2. M. Francaviglia, M. Palese, E. Winterroth, A new geometric proposal for the Hamiltonian description of classical field theories, Proc. Conf. Diff. Geom. Appl., Opava, 2001 (Math. Publications, Vol. 3, Silesian Univ. Opava, 2001) 415-423.
  3. I. Kanatchikov, Geometric (pre)quantization in the polysymplectic approach to field theory, Proc. Conf. Diff. Geom. Appl., Opava (Math. Publications, Vol. 3, Silesian Univ. Opava, 2001) 309-321.
  4. D. Smetanová, The regularity problem in the calculus of variations, PhD Thesis, Palacký University, Olomouc, 2003.
  5. A. Echevería-Enriques, J. Marin-Solano, M.C. Munoz-Lecanda, N. Román-Roy, On the construction of K-operators in field theories as sections along Legendre maps, Acta Appl. Math. 77 (2003) 1-40.
  6. D. Smetanová, On regularization of second order Lagrangians, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 289-296.
  7. A. Echeverría-Enríques, M. de León, M.C. Munoz-Lecanda and N. Román-Roy, Extended Hamiltonian systems in multisymplectic field theories, J. Math. Phys. 48 (2007) 112901, 1-30.
  8. D. Smetanová, J. Volná, P. Volný, Variational principles on fibred manifolds (in Czech), Proceedings of the Workshop "Matematika na vysokých školách" (Union of Czech Mathematicians and Physicists, Prague, 2007) 109 – 112, ISBN 978-80-01-03773-7.
  9. I. Kanatchikov, On a generalization of the Dirac bracket in the De-Donder-Weyl Hamiltonian formalism, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 615-625.
  10. X. Grácia, R. Martin and N. Román-Roy, Constraint algorithm for k-presymplectic Hamiltonian systems: Application to singular field theories, Int. J. Geom. Met. Mod. Phys. 6 (5) (2009) 851.
  11. N. Román-Roy, Multisymplectic Lagrangian and Hamiltonian formalisms of classical field theories, Symmetry, Integrability and Geometry – Methods and Applications (SIGMA) 5 Art. No. 100 (2009), 25pp.

O. Krupková, Recent results in the geometry of constrained systems, Reports on Math. Phys. 49 (2002) 269-278.

Cited in:

  1. L. Czudková and J. Musilová, Variational non-holonomic systems in physics, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 131-140.
  2. M. Swaczyna, On the nonholonomic variational principle, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 297-306.
  3. L. Czudková, J. Janová and J. Musilová, Non-holonomic mechanical systems and variational principle, In: Differential Geometry and its Applications, Proc. Conf. Prague 2004 (Charles University, Prague, 2005) 571-579.
  4. X. Grácia and R. Martín, Regularity and symmetries of nonholonomic systems, J. Phys. A: Math. Gen. 38 (2005) 1071-1087.
  5. M. Swaczyna, Variational Aspects of Nonholonomic Mechanical Systems, PhD thesis, Faculty of Science, Palacký University, Olomouc, 2005, 121 pp.
  6. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.
  7. L. Czudková, J. Janová, J. Musilová, Trivial constraint variational problem, Rend. Circ. Mat. Palermo, Serie II, Suppl. 79 (2006) 67-74.
  8. J. Janová, Mechanics of nonholonomic constrainned systems, PhD Thesis, Masaryk University, Brno, 2006.
  9. J. Janová and J. Musilová, Non-holonomic mechanics: A geometrical treatment of general coupled rolling motion, Int. J. Non-Linear Mechanics 44 (2009) 98-105.

O. Krupková and D. Smetanová, On regularization of variational problems in first order field theory, Rend. Circ. Mat. Palermo, Serie II, Suppl. 66 (2001) 133-140.

Cited in:

  1. D. Smetanová, On Hamilton p2-equations in second order field theory in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy, eds. (Debrecen University, Debrecen, 2001) 329-341.
  2. D. Smetanová, The regularity problem in the calculus of variations, PhD Thesis, Palacký University, Olomouc, 2003.
  3. A. Echevería-Enriques, J. Marin-Solano, M.C. Munoz-Lecanda, N. Román-Roy, On the construction of K-operators in field theories as sections along Legendre maps, Acta Appl. Math. 77 (2003) 1-40.
  4. D. Smetanová, On regularization of second order Lagrangians, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 289-296.
  5. A. Echeverría-Enríques, M. de León, M.C. Munoz-Lecanda and N. Román-Roy, Extended Hamiltonian systems in multisymplectic field theories, J. Math. Phys. 48 (2007) 112901, 1-30.
  6. M. Castrillón López and J. Munoz-Masqué, Lie algebra pairing and the Lagrangian and Hamiltonian equations in gauge-invariant problems, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 595-602.
  7. I. Kanatchikov, On a generalization of the Dirac bracket in the De-Donder-Weyl Hamiltonian formalism, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 615-625.
  8. X. Grácia, R. Martin and N. Román-Roy, Constraint algorithm for k-presymplectic Hamiltonian systems: Application to singular field theories, Int. J. Geom. Met. Mod. Phys. 6 (5) (2009) 851.
  9. N. Román-Roy, Multisymplectic Lagrangian and Hamiltonian formalisms of classical field theories, Symmetry, Integrability and Geometry – Methods and Applications (SIGMA) 5 Art. No. 100 (2009), 25pp.

O. Krupková and A. Vondra, On some integration methods for connections on fibered manifolds, Proc. Conf., Opava, August 1992 (Silesian University, Opava, 1993), 89-102.

Cited in:

  1. A. Vondra, Symmetries of connections on fibered manifolds, Arch. Math. (Brno) 30 (1994) 97-115.
  2. A. Vondra, Geometry of second-order connections and ordinary differential equations, Math. Bohemica 120 (1995) 145-167.
  3. A. Vondra, Towards a Geometry of Higher-Order Partial Differential Equations Represented by Connections on Fibered Manifolds, Habilitation Thesis, Masaryk University, Brno, 1995, 114 pp.
  4. M. Doupovec and A. Vondra, Some natural operations between connections on fibered manifolds, Rend. Circ. Mat. Palermo, Ser.II-Suppl. 39 (1996) 73-84.
  5. M. Doupovec and A. Vondra, Natural relations between connections in 2-fibered manifolds, in: New Developments in Differential Geometry, L. Tamássy and J. Szenthe (eds.) (Kluwer, Dordrecht, 1996) 113-130.
  6. A. Vondra, Prolongations and fields of paths for higher-order O.D.E. represented by connections on a fibered manifold, Extracta Mathematicae 11 (1996) 229-24.
  7. A. Vondra, Higher-order differential equations represented by connections on prolongations of a fibered manifold, Extracta Mathematicae 15 (3) (2000) 421-512.
  8. A. Vondra, From semisprays to connections, from geometry of regular O.D.E. in mechanics to geometry of horizontal Pfaffian P.D.E. on fibered manifolds (and vice versa), in: Proceedings of the Seminar on Differential Geometry, D. Krupka, ed., "Mathematical Publications" (Silesian University, Opava, Czechia, 2000).

O. Krupková, Partial differential equations with differential constraints, J. Differential Equations 220 (2006) 354-395.

Cited in:

  1. M. Swaczyna, Variational Aspects of Nonholonomic Mechanical Systems, PhD thesis, Faculty of Science, Palacky University, Olomouc, 2005, 121 pp.
  2. J. Vankerschaver, The momentum map for nonholonomic field theories with symmetry, Int. J. Geom. Met. Mod. Phys. 2 (2005) 1029-1041.
  3. J. Vankerschaver, F. Cantrijn, M. de Leon, Geometric aspects of nonholonomic field theories, Rep. Math. Phys. 56 (2005) 387-411.
  4. F. Cantrijn and J. Vankerschaver, The Skinner-Rusk approach for vakonomic and nonholonomic field theories, in: Differential Geometric Methods in Mechanics and Field Theory (Academia Press, Gent, 2007) 1-13.
  5. J. Vankerschaver, A class of nonholonomic kinematic constraints in elasticity, J. Phys.A: Math. Theor. 40 (2007) 3889-3913.
  6. L. Czudková and J. Musilová, Non-holonomic constraint forces in field theory in physics, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 603-613.
  7. J. Vankerschaver, A connection-theoretic approach to the analysis of symmetries of nonholonomic field theories, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 703-711.
  8. J. Janová and J. Musilová, Non-holonomic mechanics: A geometrical treatment of general coupled rolling motion, Int. J. Non-Linear Mechanics 44 (2009) 98-105.

O. Krupková, Variational metrics on R x TM and the geometry of nonconservative mechanics Math. Slovaca 44 (1994) 315-335.

Cited in:

  1. A. Vondra, Geometry of second-order connections and ordinary differential equations, Math. Bohemica 120 (1995) 145-167.
  2. A. Vondra, Towards a Geometry of Higher-Order Partial Differential Equations Represented by Connections on Fibered Manifolds, Habilitation Thesis, Masaryk University, Brno 1995, 114 pp.
  3. M. Mráz and J. Musilová, Variational compatibility of force laws, In: Proc. Conf. Diff. Geom. Appl., Brno 1998 (Masaryk Univ., Brno, 1999) 553-561.
  4. A. Vondra, Higher-order differential equations represented by connections on prolongations of a fibered manifold, Extracta Mathematicae 15 (3) (2000) 421-512.
  5. A. Vondra, From semisprays to connections, from geometry of regular O.D.E. in mechanics to geometry of horizontal Pfaffian P.D.E. on fibered manifolds (and vice versa), in: Proceedings of the Seminar on Differential Geometry, D. Krupka, ed., "Mathematical Publications" (Silesian University, Opava, Czechia, 2000).
  6. T. Mestdag, J. Szilasi and V. Toth, On the geometry of generalized Lagrange metrics, Publ. Math. Debrecen 62 (2003) 511-545.
  7. W. Sarlet, Linear connections along the tangent bundle projection, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 311-336.
  8. M. Crasmareanu, Metrizable systems of autonomous second order differential equations, Carpathian J. Math. 25 (2) (2009) 163-176.

O. Krupková, Variational metric structures, Publ. Math. Debrecen 62 (2003) 461-498.

Cited in:

  1. Z. Muzsnay, The Euler-Lagrange PDE and Finsler metrizability, Houston J. of Math. 32 (2006) 79-98.
  2. I. Bucataru, Metric nonlinear connections, Diff. Geom. Appl. 25 (2007) 335-343.
  3. J.P. Penot, Infinitesimal calculus in metric spaces, J. Geom. Phys. 57 (2007) 2455-2465.
  4. I. Bucataru and R. Miron, Finsler-Lagrange Geometry: Applications to Dynamical Systems (Editura Academiei Romane, Bucuresti, 2007), ISBN 978-973-27-1527-7.
  5. W. Sarlet, Linear connections along the tangent bundle projection, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 311-336.
  6. G.E. Prince, On the inverse problem for autoparallels, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 337-346.
  7. L. Popescu, Vector Bundles Geometry, Applications to Optimal Control, (Ed. Univ. Craiova, 2008) 200pp., ISBN 978-606-510-349-8.
  8. M. Crasmareanu, Metrizable systems of autonomous second order differential equations, Carpathian J. Math. 25 (2) (2009) 163-176.

O. Krupková and G.E. Prince, Second-order ordinary differential equations in jet bundles and the inverse problem of the calculus of variations, In: Handbook of Global Analysis, Elsevier (2008), 837-904.

Cited in:

  1. G.E. Prince and D.M. King, The inverse problem in the calculus of variations: nonexistence of Lagrangians, in: Differential Geometric Methods in Mechanics and Field Theory (Academia Press, Gent, 2007) 131-140.
  2. M. Crampin and T. Mestdag, The inverse problem for invariant Lagrangians on a Lie group, J. Lie Theory 18 (2008) 471-502.
  3. G.E.Prince, On the inverse problem for autoparallels, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 337-346.
  4. D. Krupka, Global variational theory in fibred spaces, In: Handbook of Global Analysis (Elsevier, 2008) 773-836.
  5. D.J. Saunders, Jet manifolds and natural bundles, In: Handbook of Global Analysis (Elsevier, 2008) 1035-1067.
  6. A.M. Bloch, O.E. Fernandez and T. Mestdag, Hamiltonization of nonholonomic systems and the inverse problem of the calculus of variations, Reports on Math. Phys. 63 (2009) 225-249.
  7. I. Bucataru and M.F. Dahl, Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations, J. Geom. Mech. 1 (2009) 159-180.
  8. R. Malíková, On a generalization of Helmholtz conditions, Acta Math. Univ. Ostraviensis 17 (2009) 11-21.

O. Krupková, Hamilton-Jacobi distributions, Preprint, J.E. Purkyně University Brno, 1990.

Cited in:

  1. M. Ferraris and M. Francaviglia, in: Mechanics, Analysis and Geometry: 200 Years after Lagrange, M. Francaviglia and D. Holm eds. (North Holland, Amsterdam 1991).
  2. M. Ferraris and M. Francaviglia, Conservation laws in general relativity, Classical and Quantum Gravity 9 (1992) 79-95.
  3. A. Vondra, Connections in the geometry of non-autonomous regular higher-order dynamics, PhD Thesis, Masaryk Univ., Brno, Czechoslovakia, 1991, 42 pp.
  4. A. Vondra, Symmetries of connections on fibered manifolds, Arch. Math. (Brno), 30 (1994) 97-115.
  5. A. Vondra, Towards a Geometry of Higher-Order Partial Differential Equations Represented by Connections on Fibered Manifolds, Habilitation Thesis, Masaryk Univesrity, Brno, 1995, 114 pp.
  6. A. Vondra, Prolongations and fields of paths for higher-order O.D.E. represented by connections on a fibered manifold, Extracta Mathematicae 11 (1996) 229-24.
  7. A. Vondra, From semisprays to connections, from geometry of regular O.D.E. in mechanics to geometry of horizontal Pfaffian P.D.E. on fibered manifolds (and vice versa), In: Proceedings of the Seminar on Differential Geometry, D. Krupka, ed., "Mathematical Publications" (Silesian University, Opava, Czechia, 2000).

O. Krupková, On the geometry of non-holonomic mechanical systems, In: Differential Geometry and Applications, Proc. Conf., Brno, August 1998, I. Kolář, O. Kowalski, D. Krupka and J. Slovák, Eds. (Masaryk University, Brno, 1999) 533-546.

Cited in:

  1. L. Czudková and J. Musilová, Variational non-holonomic systems in physics, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 131-140.
  2. M. Swaczyna, On the nonholonomic variational principle, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 297-306.
  3. L. Czudková, J. Janová and J. Musilová, Non-holonomic mechanical systems and variational principle, in: Differential Geometry and its Applications, Proc. Conf. Prague 2004 (Charles University, Prague, 2005) 571-579.
  4. M. Swaczyna, Variational Aspects of Nonholonomic Mechanical Systems, PhD thesis, Faculty of Science, Palacky University, Olomouc, 2005, 121 pp.
  5. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.
  6. J. Janová, Mechanics of nonholonomic constrainned systems, PhD Thesis, Masaryk University, Brno, 2006.
  7. J. Janová and J. Musilová, Non-holonomic mechanics: A geometrical treatment of general coupled rolling motion, Int. J. Non-Linear Mechanics 44 (2009) 98-105.

A. Haková and O. Krupková, Variational first-order partial differential equations, J. Differential Equations 191 (2003) 67-89.

Cited in:

  1. D. Krupka, Global variational principles: Foundations and current problems, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 3-18.
  2. J. Brajerčík, D. Krupka, Variational principles for locally variational forms, J. Math. Phys. 46 (2005) 052903.
  3. J.M. Masque, L.M.P. Coronado, Global characterization of variational first-order quasi-linear equations, Rep. Math. Phys. 56 (2005) 23-38.
  4. D.R. Grigore, On a generalization of the Poincaré-Cartan form in higher-order field theory, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 55-76.
  5. R. Vitolo, Finite order variational sequences: A short review, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 99-115.
  6. D. Krupka, Global variational theory in fibred spaces, In: Handbook of Global Analysis (Elsevier, 2008) 773-836.
  7. R. Vitolo, Variational sequences, In: Handbook of Global Analysis (Elsevier, 2008) 1115-1163.

O. Krupková and M. Swaczyna, The non-holonomic variational principle, Preprint 8/2002 GAČR 201/00/0724 (Inst. of Theoretical Physics and Astrophysics, Masaryk University, Brno, 2002) 34 pp.

Cited in:

  1. M. Swaczyna, On the nonholonomic variational principle, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 297-306.
  2. L. Czudková, J. Janová and J. Musilová, Non-holonomic mechanical systems and variational principle, in: Differential Geometry and its Applications, Proc. Conf. Prague 2004 (Charles University, Prague, 2005) 571-579.
  3. M. Swaczyna, Variational Aspects of Nonholonomic Mechanical Systems, PhD thesis, Faculty of Science, Palacky University, Olomouc, 2005, 121 pp.
  4. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.
  5. L. Czudková, J. Janová, J. Musilová, Trivial constraint variational problem, Rend. Circ. Mat. Palermo, Serie II, Suppl. 79 (2006) 67-74.
  6. J. Janová, Mechanics of nonholonomic constrainned systems, PhD Thesis, Masaryk University, Brno, 2006.

O. Krupková and P. Volný, Euler-Lagrange and Hamilton equations for non-holonomic systems in field theory. J. Phys. A, 38 (40) (2005) 8715–8745.

Cited in:

  1. F. Cantrijn and J. Vankerschaver, The Skinner-Rusk approach for vakonomic and nonholonomic field theories, in: Differential Geometric Methods in Mechanics and Field Theory (Academia Press, Gent, 2007) 1-13.
  2. E. Bibbona, L. Fatibene, M. Francaviglia, Gauge-natural parametrized variational problems, vakonomic field theories and relativistic hydrodynamics of a charged fluid, Int. J. Geom. Met. Mod. Phys. 3 (2006) 1573-1608.
  3. J. Vankerschaver, A class of nonholonomic kinematic constraints in elasticity, J. Phys. A: Math. Theor. 40 (2007) 3889-3913.
  4. E. Bibbona, L. Fatibene, M. Francaviglia, Chetaev versus vakonomic prescriptions in constrained field theories with parametrized variational calculus, J. Math. Phys. 48 (2007) 03203.
  5. J. Vankerschaver, D.M. de Diego, Symmetry aspects of nonholonomic field theories, J. Phys. A: Math. Theor. 41 (2008) 035401.
  6. V.E. Tarasov, Fractional Dynamics of Relativistic Particle, Int. J. Theor. Phys. 49 (2) (2010) 293-303.

O. Krupková, Symmetries and first integrals of time-dependent higher-order constrained systems, J. Geom. Phys. (1996) 38-58.

Cited in:

  1. A. Vondra, Towards a Geometry of Higher-Order Partial Differential Equations Represented by Connections on Fibered Manifolds, Habilitation Thesis, Masaryk University, Brno, 1995, 114 pp.
  2. M. Fliess, J. Lévine, P. Martin, P. Rouchon, Nonlinear control and diffieties, with an application to physics, Contemporary Mathematics 219 (1998), 81-98.
  3. A. Vondra, Higher-order differential equations represented by connections on prolongations of a fibered manifold, Extracta Mathematicae 15 (3) (2000) 421-512.
  4. A. Vondra, From semisprays to connections, from geometry of regular O.D.E. in mechanics to geometry of horizontal Pfaffian P.D.E. on fibered manifolds (and vice versa), in: Proceedings of the Seminar on Differential Geometry, D. Krupka, ed., "Mathematical Publications" (Silesian University, Opava, Czechia, 2000).
  5. D.R. Grigore, On a generalization of the Poincaré-Cartan form in higher-order field theory, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 55-76.

O. Krupková and J. Musilová, Non-holonomic variational systems, Reports on Math. Phys. 55 (2005) 211-220.

Cited in:

  1. M. Swaczyna, On the nonholonomic variational principle, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 297-306.
  2. L. Czudková, J. Janová and J. Musilová, Non-holonomic mechanical systems and variational principle, in: Differential Geometry and its Applications, Proc. Conf. Prague 2004 (Charles University, Prague, 2005) 571-579.
  3. L. Czudková, J. Janová, J. Musilová, Trivial constraint variational problem, Rend. Circ. Mat. Palermo, Serie II, Suppl. 79 (2006) 67-74.
  4. L. Czudková and J. Musilová, Non-holonomic constraint forces in field theory in physics, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 603-613.
  5. J. Janová and J. Musilová, Non-holonomic mechanics: A geometrical treatment of general coupled rolling motion, Int. J. Non-Linear Mechanics 44 (2009) 98-105.

O. Krupková and J. Musilová, Constraint Helmholtz conditions, Preprint 6/2002 GAČR 201/00/0724 (Inst. of Theoretical Physics and Astrophysics, Masaryk University, Brno, 2002) 10 pp.

Cited in:

  1. L. Czudková and J. Musilová, Variational non-holonomic systems in physics, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 131-140.
  2. M. Swaczyna, On the nonholonomic variational principle, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 297-306.
  3. L. Czudková, J. Janová, J. Musilová, Trivial constraint variational problem, Rend. Circ. Mat. Palermo, Serie II, Suppl. 79 (2006) 67-74.
  4. J. Janová, Mechanics of nonholonomic constrainned systems, PhD Thesis, Masaryk University, Brno, 2006.

O. Krupková and M. Swaczyna, Horizontal and contact forms on constraint manifolds, Rend. Circ. Mat. Palermo, Serie II, Suppl. 75 (2005) 259-267.

Cited in:

  1. M. Swaczyna, On the nonholonomic variational principle, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 297-306.
  2. M. Swaczyna, Variational Aspects of Nonholonomic Mechanical Systems, PhD thesis, Faculty of Science, Palacky University, Olomouc, 2005, 121 pp.
  3. J. Janová, Mechanics of nonholonomic constrainned systems, PhD Thesis, Masaryk University, Brno, 2006.
  4. M. Swaczyna, Constraint Lepage one forms in higher order mechanics with nonholonomic constraints on the dynamical space, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 689-702.

O. Krupková, Higher-order constrained systems on fibered manifolds: An exterior differential systems approach, In: New Developments in Differential Geometry, Proc. Coll. on Diff. Geom., Debrecen 1994 (Kluwer, Dordrecht, 1996) 255-278.

Cited in:

  1. D. Krupka, Global variational functionals on fibered spaces, Nonlinear Analysis 47 (2001) 2633-2642.
  2. D. Krupka, J. Musilová, Recent results in variational sequence theory, in: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P.T. Nagy and L. Tamássy (Eds.), (Debrecen University, Debrecen, 2001) 161-186.
  3. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.

D. Krupka, O. Krupková, G. Prince and W. Sarlet, Contact symmetries of the Helmholtz form, Differential Geometry and Applications 25 (2007) 518-542.

Cited in:

  1. D. Krupka, Global variational theory in fibred spaces, In: Handbook of Global Analysis (Elsevier, 2008) 773-836.
  2. R. Vitolo, Variational sequences, In: Handbook of Global Analysis (Elsevier, 2008) 1115-1163.
  3. R. Malíková, On a generalization of Helmholtz conditions, Acta Math. Univ. Ostraviensis 17 (2009) 11-21.

O. Krupková, A note on the Helmholtz conditions, In: Differential Geometry, Proc. Conf., Brno 1986, Communications (UJEP Brno 1987) 181-188.

Cited in:

  1. V.M. Filipov, V.M. Savčin, S.G. Šorochov, Variational principles for nonpotential operators (Itogi nauki i techniki, Sovremennye problemy matematiki 40, VINITI, Moscow, 1992) (in Russian).
  2. M. Mráz and J. Musilová, Variational compatibility of force laws, In: Proc. Conf. Diff. Geom. Appl., Brno 1998 (Masaryk Univ., Brno, 1999) 553-561.

O. Krupková, A Geometric Theory of Variational Ordinary Differential Equations, Habilitation Thesis, Silesian University, Opava & Masaryk University, Brno, 1995, 165 pp.

Cited in:

  1. M. de León, J. Marín-Solano and J. C. Marrero, The constraint algorithm in the jet formalism, Diff. Geom. Appl., 6 (1996) 275-299
  2. J. Janová, A geometric theory of mechanical systems with nonholonomic constraints (in Czech), Thesis, Masaryk University, Brno, 2002, 76 pp.

D. Krupka, O. Krupková, G.E. Prince, and W. Sarlet, Contact symmetries and variational sequences, In: Proc. 9th Int. Conf. on Diff. Geom. & Appl., J. Bureš, O. Kowalski, D. Krupka and J. Slovák (Eds.), Prague, August 2004 (Charles University, Prague, 2005) 605-615.

Cited in:

  1. R. Vitolo, Finite order variational sequences: A short review, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 99-115.
  2. D. Krupka, Global variational theory in fibred spaces, In: Handbook of Global Analysis (Elsevier, 2008) 773-836.

O. Krupková and P. Volný, Differential equations with constraints in jet bundles: Lagrangian and Hamiltonian systems, Lobachevskii Journal of Mathematics 23 (2006) 95-150.

Cited in:

  1. D. Smetanová, J. Volná, P. Volný, Variational principles on fibred manifolds (in Czech), Proceedings of the Workshop "Matematika na vysokých školách" (Union of the Czech Mathematicians and Physicists & Technical University in Prague, Prague, 2007) 109 – 112, ISBN 978-80-01-03773-7.
  2. J. Vankerschaver, A connection-theoretic approach to the analysis of symmetries of nonholonomic field theories, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), (World Scientific, Singapore, 2008) 703-711.

M. Štefanová and O. Štěpánková, Variationality and invariance of systems of partial differential equations, Scripta Fac. Sci. Nat. UJEP Brunensis (Physica) 5 (1985), 283-288 (based on the paper M. Štefanová and O. Štěpánková, Invariance of equations of motion and variationality conditions (in Czech), presented to and awarded prize at the Czecho-Slovac Students Scientific Conference in Mathematics and Physics, Prague, March, 1982).

Cited in:

  1. D. Krupka and J. Musilová, Constants of the motion in higher order mechanics and field theory (in Czech), Pokroky mat. fyz. a astronom. 28 (1983) 259-266.

O. Štěpánková, Generalized regularity in Hamiltonian mechanics (in Czech), paper presented to and awarded prize at the Czecho-Slovac Students Scientific Conference in Mahematics and Physics, Prague, March, 1984.

Cited in:

  1. J. Šeděnková, Representations of variational sequences and Lepage forms, PhD Thesis, Palacký University, Olomouc, 2004.

O. Krupková, Liouville and Jacobi theorems for vector distributions, In: Differential Geometry and Its Applications, Proc. Conf., Opava, August 1992, O. Kowalski and D. Krupka, Eds. (Math. Publications 1, Silesian University, Opava, Czechoslovakia, 1993) 75-88.

Cited in:

  1. D.R. Grigore, On a generalization of the Poincaré-Cartan form in higher-order field theory, In: Variations, Geometry and Physics (Nova Science Publishers, New York, 2008) 55-76.

O. Krupková, Regularity in field theory, Lecture, Conf. "New Applications of Multisymplectic Field Theory", Salamanca, September, 1999.

Cited in:

  1. D. Smetanová, The regularity problem in the calculus of variations, PhD Thesis, Palacký University, Olomouc, 2003.

O. Krupková, Differential systems in higher-order mechanics. In: Proceedings of the Seminar on Differential Geometry, Mathematical Publications 2 (Silesian University, Opava 2000) 87-130, ISBN 80-7248-104-5.

Cited in:

  1. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.

P. Volný, O. Krupková, Hamilton equations for non-holonomic systems, in: Differential Geometry and Its Applications, Proc. Conf., Opava, 2001, O. Kowalski, D. Krupka and J. Slovák, eds. (Mathematical Publications, Vol. 3, Silesian University, Opava, Czech Republic, 2001) 369-380

Cited in:

  1. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.

O. Krupková, P. Volný, Hamilton equations for non-holonomic systems in field theory, Preprint Series GACR 2001/00/0724, No. 9, Silesian University, Opava, 2002.

Cited in:

  1. P. Volný, Nonholonomic systems, PhD Thesis, Palacký University, Olomouc, 2005.

O. Krupková, Higher-order Hamiltonian field theory, Preprint, Department of Algebra and Geometry, Palacký University, Olomouc, 2004.

Cited in:

  1. D. Smetanová, On regularization of second order Lagrangians, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 289-296.

O. Krupková, Helmholtz conditions in the geometry of second order ordinary differential equations, In: Differential Geometric Methods in Mechanics and Field Theory, Volume in Honour of W. Sarlet (Academia Press, Gent, 2007) 91-114.

Cited in:

  1. D. Krupka, The structure of the Euler-Lagrange mapping, paper in honour of N.I. Lobachevskii, Russian Mathematics (Iz. VUZ) 51 (12) (2007), N.I. Lobachevskii Anniversary Volume, 52-70.

O. Krupková and G.E. Prince, Lepage Forms, Closed 2-Forms and Second-Order Ordinary Differential Equations, Russian Mathematics (Iz. VUZ) 51 (2007) 1-16.

Cited in:

  1. R. Malíková, On a generalization of Helmholtz conditions, Acta Math. Univ. Ostraviensis 17 (2009) 11-21.

O. Krupková and J. Musilová, The relativistic mechanics in a nonholonomic setting: A unified approach to particles with non-zero mass and massless particles, ARXIV 09042933v1 (2009).

Cited in:

  1. V.E. Tarasov, Fractional Dynamics of Relativistic Particle, Int. J. Theor. Phys. 49 (2) (2010) 293-303.