Discrete Routh reduction

Journal of Physics A: Mathematical and General

Volumn 39, Issue 19, 2006, Pages 5521-5544

  Jalnapurkar, Sameer M ^a   Leok, Melvin ^b   Marsden, Jerrold E ^c   West, Matthew ^d  

^a INDIAN INSTITUTE OF SCIENCE   (India)

^b UNIVERSITY OF MICHIGAN   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^d 496 Lomita Mall   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646262572     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/19/S12     Document Type: Article

References (44)

1. Benettin G, Cherubini A M and Fass F 2001 A changing-chart symplectic algorithm for rigid bodies and other Hamiltonian systems on manifolds SIAM J. Sci. Comput. 23 (4) 1189-203
2. Bobenko A, Lorbeer B and Suris Y 1998 Integrable discretizations of the Euler top J. Math. Phys. 39 6668-83
3. Bobenko A and Suris Y 1999 Discrete lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products Lett. Math. Phys. 49 79-93
4. Bobenko A I and Suris Y B 1999 Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top Commun. Math. Phys. 204 147-88
5. Borri B, Trainelli L and Bottasso C L 2000 On representations and parametrizations of motion Multibody Syst. Dyn. 4 129-93
6. Cendra H, Holm D, Marsden J and Ratiu T 1998 Lagrangian reduction, the Euler-Poincaré equations and semidirect products Am. Math. Soc. Transl. 186 1-25
7. Chang D E and Marsden J E 2003 Geometric derivation of the delaunay variables and geometric phases Celest. Mech. Dyn. Astron. 86 185-208
8. Desbrun M, Hirani A, Leok M and Marsden J 2003 Discrete exterior calculus Preprint math.DG/0508341
9. Hairer E, Lubich C and Wanner G 2001 Geometric Numerical Integration (Berlin: Springer)
10. Hairer E, Nørsett S and Wanner G 1993 Solving Ordinary Differential Equations: I. Nonstiff Problems (Springer Series in Computational Mathematics vol 8) 2nd edn (Berlin: Springer)
11. Hairer E and Wanner G 1996 Solving Ordinary Differential Equations: II. Stiff and Differential-Algebraic Problems (Springer Series in Computational Mathematics vol 14) 2nd edn (Berlin: Springer)
12. Holm D D and Lynch P 2002 Stepwise precession of the resonant swinging spring SIAM J. Appl. Dyn. Syst. 1 44-64
13. Holm D D, Marsden J E and Ratiu T S 1998 The Euler-Poincaré equations and semidirect products with applications to continuum theories Adv. Math. 137 1-81
14. Iserles A, Munthe-Kaas H, Nørsett S P and Zanna A 2000 Lie-group methods Acta Numer. 9 215-365
15. Jalnapurkar S and Marsden J 2000 Reduction of Hamilton's variational principle Dyn. Stab. Syst. 15 287-318
16. Krysl P 2005 Explicit momentum-conserving integrator for dynamics of rigid bodies approximating the midpoint Lie algorithm Int. J. Numer. Methods Eng. 63 (15) 2171-93
17. Krysl P and Endres L 2005 Explicit Newmark/Verlet algorithm for time integration of the rotational dynamics of rigid bodies Int. J. Numer. Methods Eng. 62 (15) 2154-77
18. Lee T Y, Leok M and McClamroch N H 2005 A Lie group variational integrator for the attitude dynamics of a rigid body with applications to the 3D pendulum Proc. IEEE Conf. on Control Applications pp 962-7
19. Leimkuhler B and Patrick G 1996 A symplectic integrator for Riemannian manifolds J. Nonlinear Sci. 6 367-84
20. Leok M 2004 Foundations of computational geometric mechanics Thesis California Institute of Technology
21. Leok M 2004 Generalized Galerkin variational integrators Preprint math.NA/0508360
22. Leok M, Marsden J and Weinstein A 2004 A discrete theory of connections on principal bundles Preprint math.DG/0508338
23. Lew A, Marsden J E, Ortiz M and West M 2003 Asynchronous variational integrators Arch. Ration. Mech. Anal. 167 85-146
24. Marrero J C, Martín de Diego D and Martínez E 2005 Discrete Lagrangian and Hamiltonian mechanics on Lie groupoids Preprint math.DG/0506299
25. Marsden J 1992 Lectures on Mechanics (London Mathematical Society Lecture Note Series vol 174) (Cambridge: Cambridge University Press)
26. Marsden J, Montgomery R and Ratiu T 1990 Reduction, symmetry, and phases in mechanics Mem. Am. Math. Soc. 88 1-110
27. Marsden J, Pekarsky S and Shkoller S 1999 Discrete Euler-Poincaré and Lie-Poisson equations Nonlinearity 12 1647-62
28. Marsden J, Pekarsky S and Shkoller S 2000 Symmetry reduction of discrete Lagrangian mechanics on Lie groups J. Geom. Phys. 36 140-51
29. Marsden J and Ratiu T 1999 Introduction to Mechanics and Symmetry (Texts in Applied Mathematics vol 17) 2nd edn (Berlin: Springer)
30. Marsden J, Ratiu T and Scheurle J 2000 Reduction theory and the Lagrange-Routh equations J. Math. Phys. 41 3379-429
31. Marsden J E, Ratiu T S and Weinstein A 1984 Semi-direct products and reduction in mechanics Trans. Am. Math. Soc. 281 147-77
32. Marsden J and Scheurle J 1993a Lagrangian reduction and the double spherical pendulum ZAMP 44 17-43
33. Marsden J and Scheurle J 1993b The reduced Euler-Lagrange equations Fields Inst. Commun. 1 139-64
34. Marsden J E and Scheurle J 1995 Pattern evocation and geometric phases in mechanical systems with symmetry Dyn. Stab. Syst. 10 315-38
35. Marsden J E, Scheurle J and Wendlandt J 1996 Visualization of orbits and pattern evocation for the double spherical pendulum ICIAM 95: Mathematical Research vol 87 ed K Kirchgässner, O Mahrenholtz and R Mennicken (Berlin: Academie Verlag) pp 213-32
36. Marsden J E and Weinstein A 1974 Reduction of symplectic manifolds with symmetry Rep. Math. Phys. 5 121-30
37. Marsden J and West M 2001 Discrete mechanics and variational integrators Acta Numerica vol 10 (Cambridge: Cambridge University Press)
38. Ortega J-P and Ratiu T S 2004 Momentum Maps and Hamiltonian Reduction (Progress in Mathematics vol 222) (Boston, MA: Birkhäuser)
39. Patrick G 1991 Two axially symmetric coupled rigid bodies: relative equilibria stability bifurcations and a momentum preserving symplectic integrator PhD Thesis University of California, Berkeley
40. Prussing J and Conway B 1993 Orbital Mechanics (Oxford: Oxford University Press)
41. Sanyal A, Bloch A J and McClamroch H N 2004 Dynamics of multibody systems in planar motion in a central gravitational field Dyn. Syst. Int. J. 19 (4) 303-43
42. Sanyal A, Shen J and McClamroch H N 2003 Variational integrators for mechanical systems with cyclic generalized coordinates Preprint
43. Weinstein A 1996 Lagrangian mechanics and groupoids Mechanics Days (Waterloo, ON, 1992) (Fields Institute Communications vol 7) (Providence, RI: American Mathematical Society) pp 207-31
44. Wisdom J, Peale S and Mignard F 1984 The chaotic rotation of hyperion Icarus 58 137-52