On the nonexistence of an additional integral of the motion of a star in a cluster

Details On the nonexistence of an additional integral of the motion of a star in a cluster On the nonexistence of an additional integral of the motion of a star in a cluster

Oct 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977sva....21..648b&link_type=abstract

(Astronomicheskii Zhurnal, vol. 54, Sept.-Oct. 1977, p. 1140, 1141.) Soviet Astronomy, vol. 21, Sept.-Oct. 1977, p. 648. Transla

Astronomy and Astrophysics

Astronomy

Equations Of Motion, Poincare Problem, Star Clusters, Stellar Motions, Analytic Functions, Canonical Forms, Differential Equations, Ellipsoids, 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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