Integrable Discretizations of Some Cases of the Rigid Body Dynamics

DOI

10.2991/jnmp.2001.8.4.7How to use a DOI?

Abstract

A heavy top with a fixed point and a rigid body in an ideal fluid are important examples of Hamiltonian systems on a dual to the semidirect product Lie algebra e(n) = so(n) Rn . We give a Lagrangian derivation of the corresponding equations of motion, and introduce discrete time analogs of two integrable cases of these systems: the Lagrange top and the Clebsch case, respectively. The construction of discretiztions is based on the discrete time Lagrangian mechanics on Lie groups, accompanied by the discrete time Lagrangian reduction. The resulting explicit maps on e (n) are Poisson with respect to the Lie­Poisson bracket, and are also completely integrable. Lax representations of these maps are also found.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Yuri B. Suris
PY  - 2001
DA  - 2001/11/01
TI  - Integrable Discretizations of Some Cases of the Rigid Body Dynamics
JO  - Journal of Nonlinear Mathematical Physics
SP  - 534
EP  - 560
VL  - 8
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2001.8.4.7
DO  - 10.2991/jnmp.2001.8.4.7
ID  - Suris2001
ER  -