Abstract
This paper deals with the plane motion of a star in the gravitational field of a system which is in a steady state and rotates with a constant angular velocity. For these systems a class of potentials permitting a local integral, linear with respect to the velocity components, has been found. The concept of the local integral itself was introduced by one of the authors of the present paper (Antonov, 1981). A detailed model has been constructed. The corresponding domain of the particle motion and the form of the trajectory coils have been determined. The result is compared with the motion in a more realistic potential.
Similar content being viewed by others
References
Antonov, V.A.: 1981, Vestnik Leningrad Universit., 19, (97–105) (in Russian).
Arnold, V.I.: 1971,The Ordinary Differential Equations, Nauka, Moscow (in Russian).
Courant, R. and Hilbert, D.: 1962,Methods of Mathematical Physics, vol. 2, Interscience, New York.
Gantmacher, E.R.: 1966,Lectures in Analytical Mechanics, Nauka, Moscow (in Russian).
Kravtsov, Ju.A. and Orlov, Ju.I.: 1980,Geometrical Optics of Inhomogeneous Media, Nauka, Moscow (in Russian).
Szebehely, V.: 1967,Theory of Orbits. The Restricted Problem of Three Bodies, Acad. press, New York-London.
Vlasov, A.K.: 1938,The Course of Superior Mathematics, vol. 2, Nauka, Moscow (in Russian).
Wintner, A.: 1941,Analytical Foundations of Celestial Mechanics, Princeton.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Antonov, V.A., Shamshiev, F.T. Local integrals and the plane motion of a point in rotating systems. Celestial Mech Dyn Astr 56, 451–469 (1993). https://doi.org/10.1007/BF00691813
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00691813