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Reduction of invariant constrained systems using anholonomic frames
1. | Department of Mathematics, Ghent University, Krijgslaan 281, S9, B-9000 Gent, Belgium, Belgium |
References:
[1] |
A. M. Bloch with the collaboration of J. Baillieul, P. Crouch and J. E. Marsden, "Nonholonomic Mechanics and Control,'', Springer, (2003).
|
[2] |
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. |
[3] |
A. M. Bloch, J. E. Marsden and D. V. Zenkov, Quasi-velocities and symmetries in nonholonomic systems,, Dynamical Systems, 24 (2009), 187.
doi: 10.1080/14689360802609344. |
[4] |
F. Cantrijn, J. Cortés, M. de León and D. Martín de Diego, On the geometry of generalized Chaplygin systems,, Math. Proc. Camb. Phil. Soc., 132 (2002), 323.
doi: 10.1017/S0305004101005679. |
[5] |
H. Cendra, J. E. Marsden and T. S. Ratiu, "Lagrangian Reduction by Stages,'', Memoirs of the American Mathematical Society 152, (2001).
|
[6] |
H. Cendra, J. E. Marsden and T. S. Ratiu, Geometric mechanics, Lagrangian reduction, and nonholonomic systems,, in, (2001), 221.
|
[7] |
J. Cortés Monforte, "Geometric, Control and Numerical Aspects of Nonholonomic Systems,'', Lecture Notes in Mathematics 1793, (1793).
|
[8] |
M. Crampin and T. Mestdag, Routh's procedure for non-Abelian symmetry groups,, J. Math. Phys., 49 (2008).
doi: 10.1063/1.2885077. |
[9] |
M. Crampin and T. Mestdag, Reduction and reconstruction aspects of second-order dynamical systems with symmetry,, Acta Appl. Math., 105 (2009), 241.
doi: 10.1007/s10440-008-9274-7. |
[10] |
M. Crampin and T. Mestdag, Anholonomic frames in constrained dynamics,, Dynamical Systems, 25 (2010), 159.
doi: 10.1080/14689360903360888. |
[11] |
M. Crampin and F. A. E. Pirani, "Applicable Differential Geometry,'', LMS Lecture Notes 59, (1988).
|
[12] |
R. H. Cushman, H. Duistermaat and J. Śniatycki, "Geometry of Nonholonomically Constrained Systems,'', Advanced Series in Nonlinear Dynamics 26, (2010).
|
[13] |
M. de León, J. C. Marrero and E. Martínez, Lagrangian submanifolds and dynamics on Lie algebroids,, J. Phys. A: Math. Gen., 38 (2005).
doi: 10.1088/0305-4470/38/24/R01. |
[14] |
K. Ehlers, J. Koiller, R. Montgomery and P. M. Rios, Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization,, The Breadth of Symplectic Geometry, (2005), 75.
|
[15] |
B. Jovanovic, Geometry and integrability of Euler-Poincaré-Suslov equations,, Nonlinearity, 14 (2001), 1555.
doi: 10.1088/0951-7715/14/6/308. |
[16] |
J. Koiller, Reduction of some classical non-holonomic systems with symmetry,, Arch. Rat. Mech. Anal., 118 (1992), 113.
doi: 10.1007/BF00375092. |
[17] |
O. Krupková, Mechanical systems with non-holonomic constraints,, J. Math. Phys., 38 (1997), 5098.
doi: 10.1063/1.532196. |
[18] |
J. E. Marsden and T. S. Ratiu, "Introduction to Mechanics and Symmetry,'', Texts in Applied Mathematics 17, (1999).
|
[19] |
J. E. Marsden, T. S. Ratiu and J. Scheurle, Reduction theory and the Lagrange-Routh equations,, J. Math. Phys., 41 (2000), 3379.
doi: 10.1063/1.533317. |
[20] |
T. Mestdag and M. Crampin, Invariant Lagrangians, mechanical connections and the Lagrange-Poincaré equations,, J. Phys. A: Math. Theor., 41 (2008).
doi: 10.1088/1751-8113/41/34/344015. |
[21] |
T. Mestdag and B. Langerock, A Lie algebroid framework for non-holonomic systems,, J. Phys. A: Math. Gen., 38 (2005), 1097.
doi: 10.1088/0305-4470/38/5/011. |
[22] |
J. I. Neĭmark and N. A. Fufaev, "Dynamics of Nonholonomic Systems,'', Transl. of Math. Monographs 33, (1972). Google Scholar |
[23] |
W. Sarlet, F. Cantrijn and D. J. Saunders, A geometrical framework for the study of non-holonomic Lagrangian systems,, J. Phys. A: Math. Gen., 28 (1995), 3253.
doi: 10.1088/0305-4470/28/11/022. |
[24] |
J. Vilms, Connections on tangent bundles,, J. Diff. Geom., 1 (1967), 235.
|
show all references
References:
[1] |
A. M. Bloch with the collaboration of J. Baillieul, P. Crouch and J. E. Marsden, "Nonholonomic Mechanics and Control,'', Springer, (2003).
|
[2] |
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. |
[3] |
A. M. Bloch, J. E. Marsden and D. V. Zenkov, Quasi-velocities and symmetries in nonholonomic systems,, Dynamical Systems, 24 (2009), 187.
doi: 10.1080/14689360802609344. |
[4] |
F. Cantrijn, J. Cortés, M. de León and D. Martín de Diego, On the geometry of generalized Chaplygin systems,, Math. Proc. Camb. Phil. Soc., 132 (2002), 323.
doi: 10.1017/S0305004101005679. |
[5] |
H. Cendra, J. E. Marsden and T. S. Ratiu, "Lagrangian Reduction by Stages,'', Memoirs of the American Mathematical Society 152, (2001).
|
[6] |
H. Cendra, J. E. Marsden and T. S. Ratiu, Geometric mechanics, Lagrangian reduction, and nonholonomic systems,, in, (2001), 221.
|
[7] |
J. Cortés Monforte, "Geometric, Control and Numerical Aspects of Nonholonomic Systems,'', Lecture Notes in Mathematics 1793, (1793).
|
[8] |
M. Crampin and T. Mestdag, Routh's procedure for non-Abelian symmetry groups,, J. Math. Phys., 49 (2008).
doi: 10.1063/1.2885077. |
[9] |
M. Crampin and T. Mestdag, Reduction and reconstruction aspects of second-order dynamical systems with symmetry,, Acta Appl. Math., 105 (2009), 241.
doi: 10.1007/s10440-008-9274-7. |
[10] |
M. Crampin and T. Mestdag, Anholonomic frames in constrained dynamics,, Dynamical Systems, 25 (2010), 159.
doi: 10.1080/14689360903360888. |
[11] |
M. Crampin and F. A. E. Pirani, "Applicable Differential Geometry,'', LMS Lecture Notes 59, (1988).
|
[12] |
R. H. Cushman, H. Duistermaat and J. Śniatycki, "Geometry of Nonholonomically Constrained Systems,'', Advanced Series in Nonlinear Dynamics 26, (2010).
|
[13] |
M. de León, J. C. Marrero and E. Martínez, Lagrangian submanifolds and dynamics on Lie algebroids,, J. Phys. A: Math. Gen., 38 (2005).
doi: 10.1088/0305-4470/38/24/R01. |
[14] |
K. Ehlers, J. Koiller, R. Montgomery and P. M. Rios, Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization,, The Breadth of Symplectic Geometry, (2005), 75.
|
[15] |
B. Jovanovic, Geometry and integrability of Euler-Poincaré-Suslov equations,, Nonlinearity, 14 (2001), 1555.
doi: 10.1088/0951-7715/14/6/308. |
[16] |
J. Koiller, Reduction of some classical non-holonomic systems with symmetry,, Arch. Rat. Mech. Anal., 118 (1992), 113.
doi: 10.1007/BF00375092. |
[17] |
O. Krupková, Mechanical systems with non-holonomic constraints,, J. Math. Phys., 38 (1997), 5098.
doi: 10.1063/1.532196. |
[18] |
J. E. Marsden and T. S. Ratiu, "Introduction to Mechanics and Symmetry,'', Texts in Applied Mathematics 17, (1999).
|
[19] |
J. E. Marsden, T. S. Ratiu and J. Scheurle, Reduction theory and the Lagrange-Routh equations,, J. Math. Phys., 41 (2000), 3379.
doi: 10.1063/1.533317. |
[20] |
T. Mestdag and M. Crampin, Invariant Lagrangians, mechanical connections and the Lagrange-Poincaré equations,, J. Phys. A: Math. Theor., 41 (2008).
doi: 10.1088/1751-8113/41/34/344015. |
[21] |
T. Mestdag and B. Langerock, A Lie algebroid framework for non-holonomic systems,, J. Phys. A: Math. Gen., 38 (2005), 1097.
doi: 10.1088/0305-4470/38/5/011. |
[22] |
J. I. Neĭmark and N. A. Fufaev, "Dynamics of Nonholonomic Systems,'', Transl. of Math. Monographs 33, (1972). Google Scholar |
[23] |
W. Sarlet, F. Cantrijn and D. J. Saunders, A geometrical framework for the study of non-holonomic Lagrangian systems,, J. Phys. A: Math. Gen., 28 (1995), 3253.
doi: 10.1088/0305-4470/28/11/022. |
[24] |
J. Vilms, Connections on tangent bundles,, J. Diff. Geom., 1 (1967), 235.
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