Compatibility conditions for a non-quadratic integral of motion

DOI10.1007/BF01372120zbMath0524.70003OpenAlexW4237540235MaRDI QIDQ3036748

George Bozis

Publication date: 1982

Published in: Celestial Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01372120

zbMATH Keywords

inverse problemtwo degrees of freedomnecessary and sufficient conditionsautonomous dynamical systemcompletely separablegiven integral will be second integral of motiontime-independent potential function

Mathematics Subject Classification ID

Dynamics of a system of particles, including celestial mechanics (70F99) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items

Integrable 2D time-irreversible systems with a cubic second integral, Fourth-degree polynomial integrals of a natural mechanical system on a two-dimensional torus, On Hamiltonian systems in two degrees of freedom with invariants quartic in the momenta of form p21p22⋅⋅⋅, New integrable problems in rigid body dynamics with quartic integrals, On momentum-polynomial integrals of a reversible Hamiltonian system of a certain form, Generalized Hill's problem: Some cases of complete integrability, New integrable problems in the dynamics of particle and rigid body

Cites Work

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• Modification of an equation of Szebehely
• On Szebehely's equation for the potential of a prescribed family of orbits
• The "third" Integral in the Restricted Three-Body Problem.