Integrable Systems and Confocal Quadrics

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


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.


Hyperelliptic Curve Integrable Hamiltonian System Tangency Condition Abelian Integral Neumann System 
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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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