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Variational Integrators for Hamiltonizable Nonholonomic Systems
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Linear weakly Noetherian constants of motion are horizontal gauge momenta
1. | Università di Padova, Dipartimento di Matematica Pura e Applicata, Via Trieste 63, 35121 Padova |
2. | Università di Verona, Dipartimento di Informatica, Cà Vignal 2, Strada Le Grazie 15, 37134 Verona |
References:
[1] |
C. Agostinelli, Nuova forma sintetica delle equazioni del moto di un sistema anolonomo ed esistenza di un integrale lineare nelle velocità lagrangiane,, Boll. Un. Mat. Ital. (3), 11 (1956), 1.
|
[2] |
L. Bates, H. Graumann and C. MacDonnell, Examples of gauge conservation laws in nonholonomic systems,, Rep. Math. Phys., 37 (1996), 295.
doi: 10.1016/0034-4877(96)84069-9. |
[3] |
S. Benenti, A 'user-friendly' approach to the dynamical equations of non-holonomic systems,, SIGMA Symmetry Integrability Geom. Methods Appl., 3 (2007).
|
[4] |
A. M. Bloch, P. S. Krishnaprasad, J. E. Marsden and R. M. Murray, Nonholonomic mechanical systems with symmetry,, Arch. Rational Mech. Anal., 136 (1996), 21.
doi: 10.1007/BF02199365. |
[5] |
A. M. Bloch, "Nonholonomic Mechanics and Controls,'', Interdisciplinary Applied Mathematics, 24 (2003).
doi: 10.1007/b97376. |
[6] |
A. M. Bloch, J. E. Marsden and D. V. Zenkov, Quasivelocities and symmetries in non-holonomic systems,, Dynamical Systems, 24 (2009), 187.
doi: 10.1080/14689360802609344. |
[7] |
F. Cantrjn, M. de León, M. de Diego and J. Marrero, Reduction of nonholonomic mechanical systems with symmetries,, Rep. Math. Phys., 42 (1998), 25.
doi: 10.1016/S0034-4877(98)80003-7. |
[8] |
F. Cantrjn, J. Cortés, M. de León and M. de Diego, On the geometry of generalized Chaplygin systems,, Math. Proc. Cambridge Phil. Soc., 132 (2002), 323.
|
[9] |
R. Cushman, D. Kemppainen, J. Śniatycki and L. Bates, Geometry of nonholonomic constraints,, Proceedings of the XXVII Symposium on Mathematical Physics (Toruń, 36 (1995), 275.
doi: 10.1016/0034-4877(96)83625-1. |
[10] |
M. de León, J. C. Marrero and D. Martín de Diego, Mechanical systems with nonlinear constraints,, Int. J. Th. Phys., 36 (1997), 979.
doi: 10.1007/BF02435796. |
[11] |
F. Fassò, A. Ramos and N. Sansonetto, The reaction-annihilator distribution and the nonholonomic Noether theorem for lifted actions,, Reg. Ch. Dyn., 12 (2007), 579.
doi: 10.1134/S1560354707060019. |
[12] |
F. Fassò, A. Giacobbe and N. Sansonetto, Gauge conservation laws and the momentum equation in nonholonomic mechanics,, Rep. Math. Phys., 62 (2008), 345.
doi: 10.1016/S0034-4877(09)00005-6. |
[13] |
F. Fassò, A. Giacobbe and N. Sansonetto, On the number of weakly Noetherian constants of motion of nonholonomic systems,, J. Geom. Mech., 1 (2009), 389.
|
[14] |
Il. Iliev and Khr. Semerdzhiev, Relations between the first integrals of a nonholonomic mechanical system and of the corresponding system freed of constraints,, J. Appl. Math. Mech., 36 (1972), 381.
doi: 10.1016/0021-8928(72)90049-4. |
[15] |
Il. Iliev and P. Ilija, On first integrals of a nonholonomic mechanical system,, J. Appl. Math. Mech., 39 (1975), 147.
doi: 10.1016/0021-8928(75)90046-5. |
[16] |
J. Koiller, Reduction of some classical nonholonomic systems with symmetry,, Arch. Rat. Mech. An., 118 (1992), 113.
doi: 10.1007/BF00375092. |
[17] |
C.-M. Marle, On symmetries and constants of motion in Hamiltonian systems with nonholonomic constraints,, in, 59 (2003), 223.
|
[18] |
J.-P. Ortega and T. S. Ratiu, "Momentum Maps and Hamiltonian Reduction,'', Progress in Mathematics, 222 (2004).
|
[19] |
J. Śniatycki, Nonholonomic Noether theorem and reduction of symmetries,, Rep. Math. Phys., 42 (1998), 5.
doi: 10.1016/S0034-4877(98)80002-5. |
[20] |
D. V. Zenkov, Linear conservation laws of nonholonomic systems with symmetry,, in, 2003 (2002), 967.
|
show all references
References:
[1] |
C. Agostinelli, Nuova forma sintetica delle equazioni del moto di un sistema anolonomo ed esistenza di un integrale lineare nelle velocità lagrangiane,, Boll. Un. Mat. Ital. (3), 11 (1956), 1.
|
[2] |
L. Bates, H. Graumann and C. MacDonnell, Examples of gauge conservation laws in nonholonomic systems,, Rep. Math. Phys., 37 (1996), 295.
doi: 10.1016/0034-4877(96)84069-9. |
[3] |
S. Benenti, A 'user-friendly' approach to the dynamical equations of non-holonomic systems,, SIGMA Symmetry Integrability Geom. Methods Appl., 3 (2007).
|
[4] |
A. M. Bloch, P. S. Krishnaprasad, J. E. Marsden and R. M. Murray, Nonholonomic mechanical systems with symmetry,, Arch. Rational Mech. Anal., 136 (1996), 21.
doi: 10.1007/BF02199365. |
[5] |
A. M. Bloch, "Nonholonomic Mechanics and Controls,'', Interdisciplinary Applied Mathematics, 24 (2003).
doi: 10.1007/b97376. |
[6] |
A. M. Bloch, J. E. Marsden and D. V. Zenkov, Quasivelocities and symmetries in non-holonomic systems,, Dynamical Systems, 24 (2009), 187.
doi: 10.1080/14689360802609344. |
[7] |
F. Cantrjn, M. de León, M. de Diego and J. Marrero, Reduction of nonholonomic mechanical systems with symmetries,, Rep. Math. Phys., 42 (1998), 25.
doi: 10.1016/S0034-4877(98)80003-7. |
[8] |
F. Cantrjn, J. Cortés, M. de León and M. de Diego, On the geometry of generalized Chaplygin systems,, Math. Proc. Cambridge Phil. Soc., 132 (2002), 323.
|
[9] |
R. Cushman, D. Kemppainen, J. Śniatycki and L. Bates, Geometry of nonholonomic constraints,, Proceedings of the XXVII Symposium on Mathematical Physics (Toruń, 36 (1995), 275.
doi: 10.1016/0034-4877(96)83625-1. |
[10] |
M. de León, J. C. Marrero and D. Martín de Diego, Mechanical systems with nonlinear constraints,, Int. J. Th. Phys., 36 (1997), 979.
doi: 10.1007/BF02435796. |
[11] |
F. Fassò, A. Ramos and N. Sansonetto, The reaction-annihilator distribution and the nonholonomic Noether theorem for lifted actions,, Reg. Ch. Dyn., 12 (2007), 579.
doi: 10.1134/S1560354707060019. |
[12] |
F. Fassò, A. Giacobbe and N. Sansonetto, Gauge conservation laws and the momentum equation in nonholonomic mechanics,, Rep. Math. Phys., 62 (2008), 345.
doi: 10.1016/S0034-4877(09)00005-6. |
[13] |
F. Fassò, A. Giacobbe and N. Sansonetto, On the number of weakly Noetherian constants of motion of nonholonomic systems,, J. Geom. Mech., 1 (2009), 389.
|
[14] |
Il. Iliev and Khr. Semerdzhiev, Relations between the first integrals of a nonholonomic mechanical system and of the corresponding system freed of constraints,, J. Appl. Math. Mech., 36 (1972), 381.
doi: 10.1016/0021-8928(72)90049-4. |
[15] |
Il. Iliev and P. Ilija, On first integrals of a nonholonomic mechanical system,, J. Appl. Math. Mech., 39 (1975), 147.
doi: 10.1016/0021-8928(75)90046-5. |
[16] |
J. Koiller, Reduction of some classical nonholonomic systems with symmetry,, Arch. Rat. Mech. An., 118 (1992), 113.
doi: 10.1007/BF00375092. |
[17] |
C.-M. Marle, On symmetries and constants of motion in Hamiltonian systems with nonholonomic constraints,, in, 59 (2003), 223.
|
[18] |
J.-P. Ortega and T. S. Ratiu, "Momentum Maps and Hamiltonian Reduction,'', Progress in Mathematics, 222 (2004).
|
[19] |
J. Śniatycki, Nonholonomic Noether theorem and reduction of symmetries,, Rep. Math. Phys., 42 (1998), 5.
doi: 10.1016/S0034-4877(98)80002-5. |
[20] |
D. V. Zenkov, Linear conservation laws of nonholonomic systems with symmetry,, in, 2003 (2002), 967.
|
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