The Inverse Problem of Dynamics for Systems with Non-Stationary Lagrangian

We construct a non-stationary form of the Lagrangian of a material point with a known integral of motion and given monoparametric family of evolving orbits. An equation for non-stationary space symmetrical 'potential' function of such Lagrangian is given and this stands for the analog of S...

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Bibliographic Details
Published in:Celestial mechanics and dynamical astronomy 1997-12, Vol.69 (4), p.347-355
Main Authors: Omarov, T B, Omarova, G T
Format: Article
Language:English
Subjects:
Astronomy
Celestial mechanics
Dynamical systems
Dynamics
Invariants
Inverse problems
Mathematical analysis
Orbits
Stands
Studies
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Summary:We construct a non-stationary form of the Lagrangian of a material point with a known integral of motion and given monoparametric family of evolving orbits. An equation for non-stationary space symmetrical 'potential' function of such Lagrangian is given and this stands for the analog of Szebehely's (1974) equation. As an application of the problem, an integrable equation from celestial mechanics of variable mass with use of non-perturbed orbits of evolving type is constructed. On its basis adiabatic invariants of non-stationary two-body problem containing a tangential force are found.
ISSN:0923-2958
1572-9478
DOI:10.1023/A:1008221021467