Integrable Discretizations of Some Cases of the Rigid Body Dynamics
- 10.2991/jnmp.2001.8.4.7How to use a DOI?
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.
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Cite this article
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 -