Non-holonomic integrators

Nonlinearity

Volumn 14, Issue 5, 2001, Pages 1365-1392

  Cortes J ^a   Martinez S ^a  

^a INSTITUTO DE MATEMÁTICAS Y FÍSICA FUNDAMENTAL   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035645521     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/14/5/322     Document Type: Article

References (36)

1. Anderson H 1983 Rattle: a velocity version of the shake algorithm for molecular dynamics calculations J. Comput. Phys. 52 24-34
2. Baez J C and Gilliam J W 1994 An algebraic approach to discrete mechanics Lett. Math. Phys. 31 205-12
3. Bates L and Śniatycki J 1992 Nonholonomic reduction Rep. Math. Phys. 32 99-115
4. Bloch A M, Krishnaprasad P S, Marsden J E and Murray R M 1996 Nonholonomic mechanical systems with symmetry Arch. Rational Mech. Anal. 136 21-99
5. Bobenko A I and Suris Y B 1998 Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top Commun. Math. Phys. 204 147-88
6. Cantrijn F, Cortés J, de León M and Martín de Diego D 2002 On the geometry of generalized Chaplygin systems Math. Proc. Cambridge Phil. Soc. to appear
7. Cantrijn F, de León M, Marrero J C and Martín de Diego D 1998 Reduction of nonholonomic mechanical systems with symmetries Rep. Math. Phys. 42 25-45
8. Cendra H, Marsden J E and Ratiu T S 2001 Geometric mechanics, Lagrangian reduction and nonholonomic systems Mathematics Unlimited - 2001 and Beyond ed B Enguist and W Schmid (New York: Springer) pp 221-73
9. Channell P and Scovel C 1990 Symplectic integrations of Hamiltonian Systems Nonlinearity 3 231-59
10. Cortés J and de León M 1999 Reduction and reconstruction of the dynamics of nonholonomic systems J. Phys. A: Math. Gen. 32 8615-45
11. Ge Z and Marsden J E 1988 Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators Phys. Lett. A 133 134-9
12. Gonzalez O 1996 Time integration and discrete Hamiltonian systems J. Nonlinear Sci. 6 449-67
13. Gonzalez O 1999 Mechanical systems subject to holonomic constraints: differential-algebraic formulations and conservative integration Physica D 132 165-74
14. Jay L 1996 Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems SIAM J. Num. Anal. 33 368-87
15. Kane C, Marsden J E and Ortiz M 1999 Symplectic energy momentum integrators J. Math. Phys. 40 3353-71
16. Kane C, Marsden J E, Ortiz M and West M 2000 Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems Int. J. Num. Math. Eng. 49 1295-325
17. Kelly S D and Murray R M 1995 Geometric phases and robotic locomotion J. Robotic Syst. 12 417-31
18. Kollier J 1992 Reduction of some classical non-holonomic systems with symmetry Arch. Rational Mech. Anal. 118 113-48
19. Koon W S and Marsden J E 1997 The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems Rep. Math. Phys. 40 21-62
20. Leimkuhler B J and Reich S 1994 Symplectic integration of constrained Hamiltonian systems Math. Comput. 63 589-605
21. Leimkuhler B J and Skeel R D 1994 Symplectic numerical integrators in constrained Hamiltonian systems J. Comput. Phys. 112 117-25
22. de León M, Martín de Diego D 1996 On the geometry of non-holonomic Lagrangian systems J. Math. Phys. 37 3389-414
23. de León M and Rodrigues P R 1989 Methods of Differential Geometry in Analytical Mechanics (North-Holland Mathematical Series 152) (Amsterdam: North-Holland)
24. Libermann P and Marie C-M 1987 Symplectic Geometry and Analytical Mechanics (Dordrecht: Reidel)
25. Marie C-M 1995 Reduction of constrained mechanical systems and stability of relative equilibria Commun. Math. Phys. 174 295-318
26. Marsden J E, Pekarsky S and Shkoller S 1999 Discrete Euler-Poincaré and Lie-Poisson equations Nonlinearity 12 1647-62
27. McLachlan R I and Scovel C 1996 A survey of open problems in symplectic integration Fields Inst. Commun. 10 151-80
28. Moser J and Veselov A P 1991 Discrete versions of some classical integrable systems and factorization of matrix polynomials Commun. Math. Phys. 139 217-43
29. Ostrowski J P 1995 Geometric perspectives on the mechanics and control of undulatory locomotion PhD Thesis California Institute of Technology
30. Ryckaert J, Ciccotti G and Berendsen H 1977 Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes J. Comput. Phys. 23 327-41
31. Reich S 1993 Symplectic integration of constrained Hamiltonian systems by Runge-Kutta methods Technical Report 93-13 University of British Columbia
32. Reich S 1996 Symplectic integration of constrained Hamiltonian systems by composition methods SIAM J. Numer. Anal. 33 475-91
33. Sanz-Serna J M and Calvo M 1994 Numerical Hamiltonian Problems (London: Chapman and Hall)
34. Veselov A P 1988 Integrable discrete-time systems and difference operators Funkts. Anal. Prilozhen. 22 1-13
35. Veselov A P 1991 Integrable Lagrangian correspondences and the factorization of matrix polynomials Funkts. Anal. Prilozhen. 25 38-49
36. Wendlandt J M and Marsden J E 1997 Mechanical integrators derived from a discrete variational principle Physica D 106 223-46