Nonexistence of an additional integral of motion for a star in a cluster

Details Nonexistence of an additional integral of motion for a star in a cluster Nonexistence of an additional integral of motion for a star in a cluster

Oct 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977azh....54.1140b&link_type=abstract

Astronomicheskii Zhurnal, vol. 54, Sept.-Oct. 1977, p. 1140, 1141. In Russian.

Astronomy and Astrophysics

Astronomy

Poincare Problem, Star Clusters, Stellar Motions, Astrodynamics, Canonical Forms, Differential Equations, Ellipsoids, Equations Of Motion, Existence Theorems

Scientific paper

It is shown that the conditions of Poincare's theorem on the nonexistence of a third integral of motion are fulfilled in the case of a star moving within an axisymmetric inhomogeneous ellipsoidal cluster. The conditions of Poincare's theorem are verified by considering an inhomogeneous oblate ellipsoid of revolution with homothetic layers and a given density distribution. In this analysis, the star's motion is described by a canonical system of sixth-order differential equations.

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