Collinear central configurations in the n-body problem with general homogeneous potential
In this paper we investigate the central configurations of collinear n-body problem given by the general law of attraction of the form f(r)=1/r. A method involving analysis skills of some elementary a...
In this paper we investigate the central configurations of collinear n-body problem given by the general law of attraction of the form f(r)=1/r. A method involving analysis skills of some elementary a...
On continuum dynamics
The theory of continuous dynamical systems is developed with an intrinsic geometric approach based on the action principle formulated in the velocity-time manifold. By endowing the finite dimensional ...
The theory of continuous dynamical systems is developed with an intrinsic geometric approach based on the action principle formulated in the velocity-time manifold. By endowing the finite dimensional ...
Note on the Poisson structure of the damped oscillator
J. Math. Phys. 50, 102902 (2009); doi:10.1063/1.3244216
Published 20 October 2009
You are not logged in to this journal. Log in
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.
©2009 American Institute of Physics
| History: | Received 15 April 2009; accepted 3 September 2009; published 20 October 2009 |
| Permalink: |
http://link.aip.org/link/?JMAPAQ/50/102902/1 |
| BUY THIS ARTICLE | (US$24) |
|
|
Connotea
CiteULike
del.icio.us
BibSonomy
KEYWORDS and PACS
RELATED DATABASES
PUBLICATION DATA
0022-2488 (print)
1089-7658 (online)
AIP
REFERENCES (20)
For access to fully linked references, you need to log in.
For access to fully linked references, you need to Log in.
- P. Caldirola,
Nuovo Cimento 18, 393 (1941) - E. Kanai,
Prog. Theor. Phys. 3, 440 (1948) . - M. Razavy, Classical and Quantum Dissipative Systems (Imperial College Press, London, 2005).
- A. O. Caldeira and A. J. Leggett,
Ann. Phys. 149, 374 (1983) . - H. Bateman, Phys. Rev. 38, 815 (1931).
- J. McEwan,
Found. Phys. 23, 313 (1993) . - H. Dekker,
Phys. Rep. 80, 1 (1981) . - V. K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan, J. Math. Phys. 48, 032701 (2007).
- P. Havas,
Nuovo Cimento, Suppl. 5, 363 (1957) . - S. Okubo, Phys. Rev. A 23, 2776 (1981).
- G. López,
Ann. Phys. 251, 372 (1996)
G. Lopez and P. Lopez, - V. I. Arnold, Mathematical Methods of Classical Mechanics, 2nd ed. (Springer, New York, 1989).
- A. P. Veselov,
Russ. Math. Surveys 46, 1 (1991) . - Note that in order to get the canonical bracket, we have rescaled the b=−1 case of the Poisson bracket (11) by the factor 2H(x,y)/sinh v, which is constant along each orbit of the map.
- W. H. Mills,
Pac. J. Math. 3, 209 (1953) . - A. N. W. Hone,
Phys. Lett. A 361, 341 (2007) . - R. Mickens, Nonstandard Finite Difference Models of Differential Equations (World Scientific, Singapore, 1994).
- M. Razavy,
Z. Phys. B 26, 201 (1977) . - V. Guillemin and S. Sternberg, Variations on a theme by Kepler (American Mathematial Society, Providence, 1990).
- R. Gladwin Pradeep, V. K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan, J. Math. Phys. 50, 052901 (2009).
- S. G. Rajeev,
Ann. Phys. 322, 1541 (2007) .
