Potentials admitting a new form of the third integral of motion, quadratic with respect to velocities

Details Potentials admitting a new form of the third integral of motion, quadratic with respect to velocities Potentials admitting a new form of the third integral of motion, quadratic with respect to velocities

Oct 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988velen.......86o&link_type=abstract

Leningradskii Universitet, Vestnik, Matematika, Mekhanika, Astronomiia (ISSN 0024-0850), Oct. 1988, p. 86-91. In Russian.

Physics

Celestial Bodies, Celestial Mechanics, Integral Equations, Potential Fields, Equations Of Motion, Field Theory (Physics), Orbital Mechanics

Scientific paper

A new class of potentials admitting a third integral of motion quadratic with respect to velocities is constructed with reference to the motions of such astronomical objects as planets, stars, galaxies, and star and galaxy clusters. An explicit expression is obtained for the third integral, and an equation for periodic orbits is derived. In general, the trajectories fill rectangular 'boxes', inclined at an angle of 45 deg to the coordinate axes.

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