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On the virial theorem for nonholonomic Lagrangian systems
Jacobi fields for second-order differential equations on Lie algebroids
1. | IUMA and Department of Theoretical Physics, University of Zaragoza, Spain |
2. | Department of Theoretical Physics, University of Zaragoza |
3. | IUMA and Departamento de Matemática Aplicada, Universidad de Zaragoza, 50009 Zaragoza |
References:
[1] |
J. F. Cariñena and E. Martínez, Generalized Jacobi equation and Inverse Problem in Classical Mechanics, In Group Theoretical Methods in Physics II (Moscow 1990), Nova Science Publishers, New York, 1991 |
[2] |
J. Cortés, M. de León, J. C. Marrero and E. Martínez, Nonholonomic Lagrangian systems on Lie algebroids, Discrete and Continuous Dynamical Systems A, 24 2 (2009), 213-271
doi: 10.3934/dcds.2009.24.213. |
[3] |
M. Crampin and F. A. E. Pirani, Applicable Differential Geometry, Cambridge University Press, 1986 |
[4] |
M. de León, J. C. Marrero and E. Martínez, Lagrangian submanifolds and dynamics on Lie algebroids, J. Phys. A: Math. Gen., 38 (2005), R241-R308 |
[5] |
P. Foulon, Géométrie des équations différentielles du second ordre, Ann. Inst. H. Poincaré Phys. Théor., 45 (1986), 1, 1-28 |
[6] |
L. A. Ibort and E. Martínez, Morse theory for Lagrangian systems, Unpublished (1997) |
[7] |
K. C. H. Mackenzie, General Theory of Lie Groupoids and Lie Algebroids, Cambridge University Press, 2005 |
[8] |
E. Martínez, Lagrangian Mechanics on Lie algebroids, Acta Appl. Math., 67 (2001), 295-320 |
[9] |
E. Martínez, Reduction in optimal control theory, Reports on Mathematical Physics 53 (2004), 79-90
doi: 10.1016/S0034-4877(04)90005-5. |
[10] |
E. Martínez, Classical field theory on Lie algebroids: variational aspects, J. Phys. A: Math. Gen., 38 (2005), 7145-7160
doi: 10.1088/0305-4470/38/32/005. |
[11] |
E. Martínez, Variational calculus on Lie algebroids, ESAIM: Control, Optimisation and Calculus of Variations 14 02, 2007, 356-380
doi: 10.1051/cocv:2007056. |
[12] |
E. Martínez, J. F. Cariñena and W. Sarlet, Derivations of differential forms along the tangent bundle projection. Part II, Differential Geometry and its Applications 3 (1993) 1-29 |
[13] |
P. W. Michor, The Jacobi flow, Rend. Sem. Mat. Univ. Politec. Torino 54 (1996), 365-372 |
show all references
References:
[1] |
J. F. Cariñena and E. Martínez, Generalized Jacobi equation and Inverse Problem in Classical Mechanics, In Group Theoretical Methods in Physics II (Moscow 1990), Nova Science Publishers, New York, 1991 |
[2] |
J. Cortés, M. de León, J. C. Marrero and E. Martínez, Nonholonomic Lagrangian systems on Lie algebroids, Discrete and Continuous Dynamical Systems A, 24 2 (2009), 213-271
doi: 10.3934/dcds.2009.24.213. |
[3] |
M. Crampin and F. A. E. Pirani, Applicable Differential Geometry, Cambridge University Press, 1986 |
[4] |
M. de León, J. C. Marrero and E. Martínez, Lagrangian submanifolds and dynamics on Lie algebroids, J. Phys. A: Math. Gen., 38 (2005), R241-R308 |
[5] |
P. Foulon, Géométrie des équations différentielles du second ordre, Ann. Inst. H. Poincaré Phys. Théor., 45 (1986), 1, 1-28 |
[6] |
L. A. Ibort and E. Martínez, Morse theory for Lagrangian systems, Unpublished (1997) |
[7] |
K. C. H. Mackenzie, General Theory of Lie Groupoids and Lie Algebroids, Cambridge University Press, 2005 |
[8] |
E. Martínez, Lagrangian Mechanics on Lie algebroids, Acta Appl. Math., 67 (2001), 295-320 |
[9] |
E. Martínez, Reduction in optimal control theory, Reports on Mathematical Physics 53 (2004), 79-90
doi: 10.1016/S0034-4877(04)90005-5. |
[10] |
E. Martínez, Classical field theory on Lie algebroids: variational aspects, J. Phys. A: Math. Gen., 38 (2005), 7145-7160
doi: 10.1088/0305-4470/38/32/005. |
[11] |
E. Martínez, Variational calculus on Lie algebroids, ESAIM: Control, Optimisation and Calculus of Variations 14 02, 2007, 356-380
doi: 10.1051/cocv:2007056. |
[12] |
E. Martínez, J. F. Cariñena and W. Sarlet, Derivations of differential forms along the tangent bundle projection. Part II, Differential Geometry and its Applications 3 (1993) 1-29 |
[13] |
P. W. Michor, The Jacobi flow, Rend. Sem. Mat. Univ. Politec. Torino 54 (1996), 365-372 |
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