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Integrable Systems and Confocal Quadrics

  • Yuri Fedorov
Part of the NATO ASI Series book series (NSSB, volume 331)

Abstract

A family of confocal quadrics in a projective space and the elliptic coordinates associated with these quadrics are known to be a powerful tool for explicit solving various integrable systems in terms of the Abelian integrals. Using the elliptic coordinates associated with such quadrics K. Jacobi solved the problem on the geodesics on an ellipsoid and K. Neumann [9] did the same for the problem of a mass point motion on a sphere in a force field with a quadratic potential.

Keywords

Hyperelliptic Curve Integrable Hamiltonian System Tangency Condition Abelian Integral Neumann System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Yuri Fedorov
    • 1
  1. 1.Department of Mathematics and MechanicsMoscow State UniversityMoscowRussia

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