This article is cited in 2 scientific papers (total in 2 papers)
Absolute and relative choreographies in rigid body dynamics
A. V. Borisovab, A. A. Kilinab, I. S. Mamaevab
a Institute of Computer Science
b Udmurt State University
For the classical problem of motion of a rigid body about a fixed point with zero integral of areas, the paper presents a family of solutions which are periodic in the absolute space. Such solutions are known as choreographies. The family includes the famous Delaunay solution in the case of Kovalevskaya, some particular solutions in the Goryachev–Chaplygin case and Steklov's solution. The “genealogy” of the solutions of the family, arising naturally 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 but with respect to a coordinate frame that rotates uniformly about the vertical (relative choreographies).
rigid body dynamics, periodic solutions, continuation by a parameter, bifurcation.
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A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Absolute and relative choreographies in rigid body dynamics”, Nelin. Dinam., 1:1 (2005), 123–141
Citation in format AMSBIB
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper Absolute and relative choreographies in rigid body dynamics
\jour Nelin. Dinam.
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This publication is cited in the following articles:
A. A. Kilin, “Metody vysokotochnogo integrirovaniya i effektivizatsiya vychislenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2009, no. 1, 153–161
A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Topology and stability of integrable systems”, Russian Math. Surveys, 65:2 (2010), 259–318
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