Applications of the Lie theory of extended groups in Hamiltonian mechanics: the oscillator and the Kepler problem

DOI10.1017/S0334270000000151zbMath0479.70020WikidataQ115335789 ScholiaQ115335789MaRDI QIDQ3938561

Peter G. L. Leach

Publication date: 1981

Published in: The Journal of the Australian Mathematical Society. Series B. Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

symmetriesfirst integralsKepler problemNoether's theoremLie theory of extended groupsthree- dimensional oscillatorvelocity- dependent transformations

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

Related Items

Cubic first integrals of autonomous dynamical systems in E2 by an algorithmic approach, FIRST INTEGRALS ASSOCIATED WITH THE ADDITIONAL SYMMETRY OF CENTRAL FORCE PROBLEMS WITH POWER LAW POTENTIALS, THE LINEAR SYMTRIES OF A NONLINEAR DIFFERENTIAL EQUATION, Relations between symmetries and conservation laws for difference systems, A Basis of Conservation Laws for Partial Differential Equations, Maximal subalgebra associated with a first integral of a system possessing sl(3,R) algebra, CONSERVATION LAWS FOR THE MONOPOLE OSCILLATOR PROBLEM, Preface to the special issue on the tercentenary of the Laplace-Runge-Lenz vector, On the Hojman conservation quantities in cosmology, Symmetry group classification of ordinary differential equations: Survey of some results, Partial Noether operators and first integrals via partial Lagrangians, Symmetries of Hamiltonian systems with two degrees of freedom, Noetherian first integrals, Generalisations of the LaplaceRungeLenz Vector, Single resonance integrals for two-dimensional Hamiltonians, Integrable time-dependent central potentials, Integrability of Toda lattice by generalized variational symmetry approach, A complex Lie-symmetry approach to calculate first integrals and their numerical preservation, Noether's theorem and symmetry, Dynamical symmetries of the geodesic equation, The invariance of the restricted problem of three bodies