Second-order systems with Runge-Lenz-type vectors

DOI10.1007/BF00403472zbMath0634.70007MaRDI QIDQ1097055

Gerard Thompson

Publication date: 1987

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

motioncharge monopole problemsCoulomb-Kepler systemexistence of a second integralmotion quadratic in momentaRunge-Lenz-type vector

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Two-body problems (70F05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

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FIRST INTEGRALS ASSOCIATED WITH THE ADDITIONAL SYMMETRY OF CENTRAL FORCE PROBLEMS WITH POWER LAW POTENTIALS ⋮ CONSERVATION LAWS FOR THE MONOPOLE OSCILLATOR PROBLEM ⋮ Generalisations of the LaplaceRungeLenz Vector

Cites Work

• Tangent bundle geometry Lagrangian dynamics
• Polynomial constants of motion in flat space
• Killing tensors in spaces of constant curvature
• The O(3,1) symmetry problem of the charge–monopole interaction