Ermakov systems, velocity dependent potentials, and nonlinear superposition

DOI10.1063/1.524758zbMath0496.70039OpenAlexW1999706740MaRDI QIDQ3960197

James L. Reid, John R. Ray

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1063/1.524758

zbMATH Keywords

two degrees of freedomnonlinear superpositionErmakov systems, velocity dependent potentialsnonlinear normal frequencies

Mathematics Subject Classification ID

Nonlinear dynamics in mechanics (70K99) Lagrange's equations (70H03)

Related Items (10)

Perturbations of Lagrangian systems based on the preservation of subalgebras of Noether symmetries ⋮ Time-dependent invariants and quantum mechanics in two dimensions ⋮ Hypercomplex analysis and integration of systems of ordinary differential equations ⋮ GENERALIZED ERMAKOV SYSTEMS IN TERMS OFsl(2,R) INVARIANTS ⋮ Canonical transformations and exact invariants for dissipative systems ⋮ An inverse problem in Lagrangian dynamics based on the preservation of symmetry groups: application to systems with a position-dependent mass ⋮ Ermakov systems: A group-theoretic approach ⋮ Ermakov systems, exact solution, and geometrical angles and phases ⋮ Two-dimensional time-dependent Hamiltonian systems with an exact invariant ⋮ Classification scheme for two-dimensional Ermakov-type systems and generalizations

Cites Work

• Symmetries of the time-dependent N-dimensional oscillator
• Ermakov systems, nonlinear superposition, and solutions of nonlinear equations of motion
• An application of Ray–Reid invariants
• Noether’s theorem, time-dependent invariants and nonlinear equations of motion

This page was built for publication: Ermakov systems, velocity dependent potentials, and nonlinear superposition