On the motion of a heavy rigid body in an ideal fluid with circulation

Alexey V Borisov; Ivan S Mamaev

doi:10.1063/1.2166530

On the motion of a heavy rigid body in an ideal fluid with circulation

Chaos. 2006 Mar;16(1):013118. doi: 10.1063/1.2166530.

Authors

Alexey V Borisov¹, Ivan S Mamaev

Affiliation

¹ Institute of Computer Science, Udmurt State University, 1 Universitetskaya Street, 426034 Izhevsk, Russia. borisov@rcd.ru

PMID: 16599749
DOI: 10.1063/1.2166530

Abstract

We consider Chaplygin's equations [Izd. Akad. Nauk SSSR 3, 3 (1933)] describing the planar motion of a rigid body in an unbounded volume of an ideal fluid while circulation around the body is not zero. Hamiltonian structures and new integrable cases are revealed; certain remarkable partial solutions are found and their stability is examined. The nonintegrability of the system describing the motion of a body in the field of gravity is proved and the chaotic behavior of the system is illustrated.