Integrable discretizations of some cases of the rigid body dynamics

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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 discretizations 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 Lie–Poisson bracket, and are also completely integrable. Lax representations of these maps are also found.

Original languageEnglish
Pages (from-to)534-560
Number of pages27
JournalJournal of Nonlinear Mathematical Physics
Volume8
Issue number4
DOIs
StatePublished - 2001
Externally publishedYes

Fingerprint

Dive into the research topics of 'Integrable discretizations of some cases of the rigid body dynamics'. Together they form a unique fingerprint.

Cite this