Integrable cases of the Hamilton-Jacobi equation and some time-dependent problems in celestial mechanics

Details Integrable cases of the Hamilton-Jacobi equation and some time-dependent problems in celestial mechanics Integrable cases of the Hamilton-Jacobi equation and some time-dependent problems in celestial mechanics

Jun 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978azh....55..635b&link_type=abstract

Astronomicheskii Zhurnal, vol. 55, May-June 1978, p. 635-644. In Russian.

Astronomy and Astrophysics

Astronomy

1

Celestial Mechanics, Hamilton-Jacobi Equation, Three Body Problem, Variable Mass Systems, Friction, Measure And Integration

Scientific paper

Several novel cases are identified where the Hamilton-Jacobi equation can be integrated. Two theorems, and their proofs, are given which demonstrate that the Hamilton-Jacobi equation has a complete integral in the cases noted. As examples, two problems are analyzed: the problem of two fixed centers of varying mass in the presence of some additional 'friction' force that is proportional to velocity and the plane restricted three-body problem in which the gravitating masses vary with time in accordance with Meshchersky's first law and then at the same rate.

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