This article is cited in 6 papers

Non-degenerate energy surfaces of rigid body in two constant fields

M. P. Kharlamov^a, D. B. Zotev<sup>b

a</sup> Volgograd Academy of Public Administration, 8, Gagarina St., 400131, Volgograd, Russia
^b Volgograd State Technical University, 128, Lenina St., 400131, Volgograd, Russia

Abstract: The problem of motion of a rigid body in two constant fields is considered. The motion is described by the Hamiltonian system with three degrees of freedom. This system in general case does not have any explicit symmetry groups and, therefore, cannot be reduced to a family of systems with two degrees of freedom. The critical points of the energy integral are found. It appeared that the energy of the system is a Morse function and has exactly four distinct critical points with different critical values and Morse indexes 0,1,2,3. In particular, the body has four equilibria, only one of which is stable. Basing on the Morse theory the smooth type of 5-dimensional non-degenerate iso-energetic manifolds is pointed out.

Keywords: rigid body, two constant fields, iso-energetic manifolds.

MSC: 70E17, 70G40

Received: 14.02.2005
Accepted: 28.02.2005

Language: English

DOI: 10.1070/RD2005v010n01ABEH000296

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