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Damped harmonic oscillator; explicitly time-dependent Lagrangian representation; Noether symmetries; conservation laws.

We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of the damped harmonic oscillator representing it by an explicitly time-dependent Lagrangian and found that a five-parameter group of transformations leaves the action integral invariant. Amongst the associated conserved quantities only two are found to be functionally independent. These two conserved quantities determine the solution of the problem and correspond to a two-parameter Abelian subgroup.

Amitava Choudhuri¹ Subrata Ghosh¹ B Talukdar¹

1. Department of Physics, Visva-Bharati University, Santiniketan 731 235, India

Published

April 2008

Manuscript received

21 June 2007

Manuscript revised

1 October 2007

Accepted

20 November 2007