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A completely integrable case in three-particle problems with homogeneous potentials

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Abstract

Trajectory equations are considered for classical three-particle problems on a straight line with potentials that are homogeneous coordinate functions. It is proposed to consider the case of a zero total energy as a completely integrable one in a generalized sense, since in it the order of the differential trajectory equation is lowered to the first one, the variables in the Hamiltonian-Jacobi equation are separated, there are additional first integral and invariant tori, in spite of the fact that the system cannot be integrable by the Liouville-Arnold theorem. The solutions are constructed (i) in a parametric form, (ii) in the form of a convergent perturbative series of a new type, and (iii) as a convergent Fourier series.

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  1. Laboratory of Theoretical Physics, Head Post Office, P.O. Box 79, 10100, Moscow, USSR

    P. P. Fiziev

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  1. P. P. Fiziev
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Fiziev, P.P. A completely integrable case in three-particle problems with homogeneous potentials. Letters in Mathematical Physics 12, 267–275 (1986). https://doi.org/10.1007/BF00402659

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  • DOI: https://doi.org/10.1007/BF00402659

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