On the motion of a heavy rigid body in an ideal fluid with circulation.
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.
Borisov
Alexey V
AV
Institute of Computer Science, Udmurt State University, 1 Universitetskaya Street, 426034 Izhevsk, Russia. borisov@rcd.ru
Mamaev
Ivan S
IS