FIRST INTEGRALS ASSOCIATED WITH THE ADDITIONAL SYMMETRY OF CENTRAL FORCE PROBLEMS WITH POWER LAW POTENTIALS

DOI10.1080/16073606.1991.9631646zbMath0736.34008OpenAlexW2045558983MaRDI QIDQ3981989

V. M. Gorringe, Peter G. L. Leach

Publication date: 26 June 1992

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/16073606.1991.9631646

zbMATH Keywords

symmetryHamilton-Jacobi theoryfirst integralscentral force problemspower law potentials

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Hamilton-Jacobi equations in mechanics (70H20) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

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Preface to the special issue on the tercentenary of the Laplace-Runge-Lenz vector, Generalisations of the LaplaceRungeLenz Vector

Cites Work

• Integrals of motion for the classical two-body problem with drag
• Second-order systems with Runge-Lenz-type vectors
• The relationship between the symmetries of and the existence of conserved vectors for the equation r^..+f(r)L+g(r)r=0
• Classes of potentials of time-dependent central force fields which possess first integrals quadratic in the momenta
• A note on the invariants for the time-dependent oscillator
• On the Lie symmetries of the classical Kepler problem
• Applications of the Lie theory of extended groups in Hamiltonian mechanics: the oscillator and the Kepler problem
• An analytic solution to the classical two-body problem with drag