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Discrete second order constrained Lagrangian systems: First results
Lagrange-Poincaré reduction in affine principal bundles
1. | ICMAT (CSIC-UAM-UC3M-UAM), Dpto. Geometría y Topología, Universidad Complutense de Madrid, 28040 Madrid, Spain |
2. | Dpto. Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, Spain |
3. | IUFFyM-USAL and Real Academia de Ciencias, Plaza de la Merced 1-4, 37008 Salamanca |
References:
[1] |
M. Castrillón López, P. L. García Pérez and T. S. Ratiu, Euler-Poincaré reduction on principal bundles, Lett. Math. Phys., 58 (2001), 167-180.
doi: 10.1023/A:1013303320765. |
[2] |
M. Castrillón López, P. L. García Pérez and C. Rodrigo, Euler-Poincaré reduction in principal fibre bundles and the problem of Lagrange, Differential Geom. Appl., 25 (2007), 585-593.
doi: 10.1016/j.difgeo.2007.06.007. |
[3] |
M. Castrillón López, P. L. García Pérez and C. Rodrigo, Euler-Poincaré reduction in principal bundles by a subgroup of the structure group, J. Geom. Phys., 74 (2013), 352-369.
doi: 10.1016/j.geomphys.2013.08.008. |
[4] |
M. Castrillón López and J. Muñoz Masqué, The geometry of the bundle of connections, Math. Z., 236 (2001), 797-811. |
[5] |
M. Castrillón López and T. S. Ratiu, Reduction in principal bundles: Covariant Lagrange-Poincaré equations, Comm. Math. Phys., 236 (2003), 223-250.
doi: 10.1007/s00220-003-0797-5. |
[6] |
M. Castrillón López, T. S. Ratiu and S. Shkoller, Reduction in principal fiber bundles: Covariant Euler-Poincaré equations, Proc. Amer. Math. Soc., 128 (2000), 2155-2164.
doi: 10.1090/S0002-9939-99-05304-6. |
[7] |
D. C. P. Ellis, F. Gay-Balmaz, D. D. Holm, V. Putkaradze and T. S. Ratiu, Symmetry reduced dynamics of charged molecular strands, Arch. Ration. Mech. Anal., 197 (2010), 811-902.
doi: 10.1007/s00205-010-0305-y. |
[8] |
D. C. P. Ellis, F. Gay-Balmaz, D. D. Holm and T. S. Ratiu, Lagrange-Poincaré field equations, J. Geom. Phys., 61 (2011), 2120-2146.
doi: 10.1016/j.geomphys.2011.06.007. |
[9] |
P. L. García, Gauge algebras, curvature and symplectic structure, J. Differential Geometry, 12 (1977), 209-227. |
[10] |
P. L. García, The Poincaré-Cartan invariant in the calculus of variations, in Symposia Mathematica, Vol. XIV (Convegno di Geometria Simplettica e Fisica Matematica, INDAM, Rome, 1973), Academic Press, London, 1974, 219-246. |
[11] |
P. L. García, A. García and C. Rodrigo, Cartan forms for first order constrained variational problems, J. Geom. Phys., 56 (2006), 571-610.
doi: 10.1016/j.geomphys.2005.04.002. |
[12] |
H. Goldschmidt and S. Sternberg, The Hamilton-Cartan formalism in the calculus of variations, Ann. Inst. Fourier (Grenoble), 23 (1973), 203-267.
doi: 10.5802/aif.451. |
[13] |
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry. Vol. I, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963. |
[14] |
S. Sternberg, Lectures on Differential Geometry, Second edition, Chelsea Publishing Co., New York, 1983. |
show all references
References:
[1] |
M. Castrillón López, P. L. García Pérez and T. S. Ratiu, Euler-Poincaré reduction on principal bundles, Lett. Math. Phys., 58 (2001), 167-180.
doi: 10.1023/A:1013303320765. |
[2] |
M. Castrillón López, P. L. García Pérez and C. Rodrigo, Euler-Poincaré reduction in principal fibre bundles and the problem of Lagrange, Differential Geom. Appl., 25 (2007), 585-593.
doi: 10.1016/j.difgeo.2007.06.007. |
[3] |
M. Castrillón López, P. L. García Pérez and C. Rodrigo, Euler-Poincaré reduction in principal bundles by a subgroup of the structure group, J. Geom. Phys., 74 (2013), 352-369.
doi: 10.1016/j.geomphys.2013.08.008. |
[4] |
M. Castrillón López and J. Muñoz Masqué, The geometry of the bundle of connections, Math. Z., 236 (2001), 797-811. |
[5] |
M. Castrillón López and T. S. Ratiu, Reduction in principal bundles: Covariant Lagrange-Poincaré equations, Comm. Math. Phys., 236 (2003), 223-250.
doi: 10.1007/s00220-003-0797-5. |
[6] |
M. Castrillón López, T. S. Ratiu and S. Shkoller, Reduction in principal fiber bundles: Covariant Euler-Poincaré equations, Proc. Amer. Math. Soc., 128 (2000), 2155-2164.
doi: 10.1090/S0002-9939-99-05304-6. |
[7] |
D. C. P. Ellis, F. Gay-Balmaz, D. D. Holm, V. Putkaradze and T. S. Ratiu, Symmetry reduced dynamics of charged molecular strands, Arch. Ration. Mech. Anal., 197 (2010), 811-902.
doi: 10.1007/s00205-010-0305-y. |
[8] |
D. C. P. Ellis, F. Gay-Balmaz, D. D. Holm and T. S. Ratiu, Lagrange-Poincaré field equations, J. Geom. Phys., 61 (2011), 2120-2146.
doi: 10.1016/j.geomphys.2011.06.007. |
[9] |
P. L. García, Gauge algebras, curvature and symplectic structure, J. Differential Geometry, 12 (1977), 209-227. |
[10] |
P. L. García, The Poincaré-Cartan invariant in the calculus of variations, in Symposia Mathematica, Vol. XIV (Convegno di Geometria Simplettica e Fisica Matematica, INDAM, Rome, 1973), Academic Press, London, 1974, 219-246. |
[11] |
P. L. García, A. García and C. Rodrigo, Cartan forms for first order constrained variational problems, J. Geom. Phys., 56 (2006), 571-610.
doi: 10.1016/j.geomphys.2005.04.002. |
[12] |
H. Goldschmidt and S. Sternberg, The Hamilton-Cartan formalism in the calculus of variations, Ann. Inst. Fourier (Grenoble), 23 (1973), 203-267.
doi: 10.5802/aif.451. |
[13] |
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry. Vol. I, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963. |
[14] |
S. Sternberg, Lectures on Differential Geometry, Second edition, Chelsea Publishing Co., New York, 1983. |
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