Non-standard conserved Hamiltonian structures in dissipative/damped systems : Nonlinear generalizations of damped harmonic oscillator

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dc.creatorPradeep, R Gladwin
dc.creatorChandrasekar, V K
dc.creatorSenthilvelan, M
dc.creatorLakshmanan, M
dc.date2008-10-10
dc.date2009-04-13
dc.date.accessioned2026-07-07T13:02:16Z
dc.date.available2026-07-07T13:02:16Z
dc.descriptionIn this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden type nonlinear oscillator equation with linear forcing, $\ddot{x}+αx\dot{x}+βx^3+γx=0,$ which preserves the form of the time independent integral, conservative Hamiltonian and the equation of motion. Generalizing this transformation we prove the existence of non-standard conservative Hamiltonian structure for a general class of damped nonlinear oscillators including Liénard type systems. Further, using the above Hamiltonian structure for a specific example namely the generalized modified Emden equation $\ddot{x}+αx^q\dot{x}+βx^{2q+1}=0$, where $α$, $β$ and $q$ are arbitrary parameters, the general solution is obtained through appropriate canonical transformations. We also present the conservative Hamiltonian structure of the damped Mathews-Lakshmanan oscillator equation. The associated Lagrangian description for all the above systems is also briefly discussed.
dc.descriptionAccepted for publication in J. Math. Phys
dc.identifierhttps://arxiv.org/abs/0810.1819
dc.identifierhttp://arxiv.org/abs/0810.1819
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/226395
dc.subjectExactly Solvable and Integrable Systems
dc.titleNon-standard conserved Hamiltonian structures in dissipative/damped systems : Nonlinear generalizations of damped harmonic oscillator
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