Complex Representation of Planar Motions and Conserved Quantities of the Kepler and Hooke Problems

DOI10.1142/S1402925110000726zbMath1377.70039MaRDI QIDQ3161580

Hervé Mohrbach, Alain Bérard, Yves Grandati

Publication date: 15 October 2010

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

conserved quantitiescomplex representationplanar motionsBohlin-Arnold-Vassiliev duality

Mathematics Subject Classification ID

Three-body problems (70F07) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (2)

Duality properties of Gorringe-Leach equations ⋮ Fradkin-Bacry-Ruegg-Souriau perihelion vector for Gorringe-Leach equations

Cites Work

• Unnamed Item
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• Duality properties of Gorringe-Leach equations
• The Kepler canonical transformations of the extended phase space
• A NOTE ON QUANTUM BOHLIN TRANSFORMATION
• Conformal transformations and the application of complex variables in mechanics and quantum mechanics
• An algorithm to relate general solutions of different bidimensional problems
• A generalisation of the Runge-Lenz constant of classical motion in a central potential
• Equivalent potentials in classical mechanics
• A Visit to the Newtonian N-Body Problem via Elementary Complex Variables
• Newton and the Transmutation of Force
• A solvable non-central perturbation of the Kepler problem
• Generalisations of the LaplaceRungeLenz Vector
• Arnol’d’s transformation—An example of a generalized canonical transformation
• Invariants at fixed and arbitrary energy. A unified geometric approach
• Planetary Motion and the Duality of Force Laws
• Three-Dimensional Isotropic Harmonic Oscillator and SU3
• On the Problem of Degeneracy in Quantum Mechanics

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