Note on the Poisson structure of the damped oscillator
- Isaac Newton Institute for Mathematical Sciences, Clarkson Road, Cambridge, CB3 0EH (United Kingdom)
The damped harmonic oscillator is one of the most studied systems with respect to the problem of quantizing dissipative systems. Recently Chandrasekar et al. [J. Math. Phys. 48, 032701 (2007)] applied the Prelle-Singer method to construct conserved quantities and an explicit time-independent Lagrangian and Hamiltonian structure for the damped oscillator. Here we describe the associated Poisson bracket which generates the continuous flow, pointing out that there is a subtle problem of definition on the whole phase space. The action-angle variables for the system are also presented, and we further explain how to extend these considerations to the discrete setting. Some implications for the quantum case are briefly mentioned.
- OSTI ID:
- 21294393
- Journal Information:
- Journal of Mathematical Physics, Vol. 50, Issue 10; Other Information: DOI: 10.1063/1.3244216; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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