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Nelin. Dinam., 2005, Volume 1, Number 1, Pages 123–141 (Mi nd193)  

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

Abstract: 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).

Keywords: rigid body dynamics, periodic solutions, continuation by a parameter, bifurcation.

Full text: PDF file (401 kB)

Document Type: Article
UDC: 531.38

Citation: 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
\Bibitem{BorKilMam05}
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper Absolute and relative choreographies in rigid body dynamics
\jour Nelin. Dinam.
\yr 2005
\vol 1
\issue 1
\pages 123--141
\mathnet{http://mi.mathnet.ru/nd193}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Kilin, “Metody vysokotochnogo integrirovaniya i effektivizatsiya vychislenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2009, no. 1, 153–161  mathnet
    2. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Topology and stability of integrable systems”, Russian Math. Surveys, 65:2 (2010), 259–318  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Нелинейная динамика
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