The Adiabatic Invariant of the Linear or Nonlinear Oscillator

DOI10.1063/1.1665263zbMath0215.28601OpenAlexW2045077849MaRDI QIDQ5618240

Keith Symon

Publication date: 1970

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

Full work available at URL: https://doi.org/10.1063/1.1665263

Mathematics Subject Classification ID

Free motion of a rigid body (70E15)

Related Items (14)

Invariants and approximate solutions for certain non-linear oscillators by means of the field method ⋮ Hamiltonian approach to the existence of magnetic surfaces ⋮ Time-dependent invariant associated to nonlinear Schrödinger–Langevin equations ⋮ Application of the Hamilton-Jacobi method to the study of rheo-linear oscillators ⋮ Energy evolution in the time-dependent harmonic oscillator with arbitrary external forcing ⋮ Ermakov systems, exact solution, and geometrical angles and phases ⋮ Quantum integrals of motion for variable quadratic Hamiltonians ⋮ On nonlinear transformations for time-dependent polynomial Hamiltonians ⋮ Application of Hamilton-Jacobi theory to the Lotka-Volterra oscillator ⋮ Class of Hamiltonians with one degree-of-freedom allowing application of Kruskal's asymptotic theory in closed form. I ⋮ Class of Hamiltonians with one degree-of-freedom allowing application of Kruskal's asymptotic theory in closed form. II ⋮ Energy Evolution in Time-Dependent Harmonic Oscillator ⋮ Dynamical Noether invariants for time-dependent nonlinear systems ⋮ Adiabatic invariants for the nonconservative Kepler's problem

Cites Work

• Theory of the alternating-gradient synchrotron
• The nonconstancy of the adiabatic invariants
• Adiabatic Invariant of the Harmonic Oscillator
• Class of Exact Invariants for Classical and Quantum Time-Dependent Harmonic Oscillators

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