Phase-Space Metric for Non-Hamiltonian Systems

Abstract

We consider an invariant skew-symmetric phase-space metric for non-Hamiltonian systems. We say that the metric is an invariant if the metric tensor field is an integral of motion. We derive the time-dependent skew-symmetric phase-space metric that satisfies the Jacobi identity. The example of non-Hamiltonian systems with linear friction term is considered.

12 pages

References in corpus (6)

• Fractional Generalization of Liouville Equations
• Fractional Systems and Fractional Bogoliubov Hierarchy Equations
• Quantization of non-Hamiltonian and Dissipative Systems
• Pure Stationary States of Open Quantum Systems
• Stationary States of Dissipative Quantum Systems
• Classical Canonical Distribution for Dissipative Systems

Cited by in corpus (9)

• Fractional Generalization of Gradient and Hamiltonian Systems
• Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
• Non-Hamiltonian Commutators in Quantum Mechanics
• Transport Equations from Liouville Equations for Fractional Systems
• Multipole Moments of Fractal Distribution of Charges
• Liouville's Theorem and the canonical measure for nonconservative systems from contact geometry
• On the Geometry and Entropy of Non-Hamiltonian Phase Space
• Phase space structure and dynamics for the Hamiltonian isokinetic thermostat
• Linear frictional forces cause orbits to neither circularize nor precess