Time-dependent dynamical symmetries and constants of motion. III. Time-dependent harmonic oscillator

DOI10.1063/1.523401zbMath0367.70004OpenAlexW2029137303MaRDI QIDQ4144229

Gerald H. Katzin, Jack Levine

Publication date: 1977

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

Full work available at URL: https://doi.org/10.1063/1.523401

Mathematics Subject Classification ID

Dynamics of a system of particles, including celestial mechanics (70F99) Nonlinear dynamics in mechanics (70K99) Lagrange's equations (70H03)

Related Items (8)

Characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems. I. Velocity-dependent mappings of second-order differential equations ⋮ Ermakov systems, Noether's theorem and the Sarlet-Bahar method ⋮ Characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems. IV. Classical (velocity-independent) mappings of second-order differential equations ⋮ Time-dependent vector constants of motion, symmetries, and orbit equations for the dynamical system r̈=îr{[Ü(t)/U(t)r −[μ/U(t)]r−2}] ⋮ Ermakov systems, nonlinear superposition, and solutions of nonlinear equations of motion ⋮ The complete symmetry group of the one-dimensional time-dependent harmonic oscillator ⋮ Integrable time-dependent central potentials ⋮ Classification scheme for two-dimensional Ermakov-type systems and generalizations

Cites Work

• Time−dependent dynamical symmetries, associated constants of motion, and symmetry deformations of the Hamiltonian in classical particle systems
• A gauge invariant formulation of time-dependent dynamical symmetry mappings and associated constants of motion for Lagrangian particle mechanics. I
• Dynamical symmetries and constants of the motion for classical particle systems
• Three-Dimensional Isotropic Harmonic Oscillator and SU3
• Class of Exact Invariants for Classical and Quantum Time-Dependent Harmonic Oscillators
• Curvature Collineations: A Fundamental Symmetry Property of the Space-Times of General Relativity Defined by the Vanishing Lie Derivative of the Riemann Curvature Tensor
• Asymptotic Theory of Hamiltonian and other Systems with all Solutions Nearly Periodic
• Groups of motions in conformally flat spaces

This page was built for publication: Time-dependent dynamical symmetries and constants of motion. III. Time-dependent harmonic oscillator