Regular and Chaotic Dynamics

, Volume 13, Issue 3, pp 204–220 | Cite as

Absolute and relative choreographies in rigid body dynamics

Research Articles

Abstract

For the classical problem of motion of a rigid body about a fixed point with zero area integral, we present a family of solutions that are periodic in the absolute space. Such solutions are known as choreographies. The family includes the well-known Delone solutions (for the Kovalevskaya case), some particular solutions for the Goryachev-Chaplygin case, and the Steklov solution. The “genealogy” of solutions of the family naturally appearing from the energy continuation and their connection with the Staude rotations are considered. It is shown that if the integral of areas is zero, the solutions are periodic with respect to a coordinate frame that rotates uniformly about the vertical (relative choreographies).

Key words

rigid-body dynamics periodic solutions continuation by a parameter bifurcation 

MSC2000 numbers

76B47 37J35 70E40 

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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia

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