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.
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© 1994 Springer Science+Business Media New York
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Fedorov, Y. (1994). Integrable Systems and Confocal Quadrics. In: Seimenis, J. (eds) Hamiltonian Mechanics. NATO ASI Series, vol 331. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0964-0_38
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DOI: https://doi.org/10.1007/978-1-4899-0964-0_38
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