Symmetries and conservation laws of the damped harmonic oscillator

Pramana

B Talukdar1¹  Amitava Choudhuri¹  Subrata Ghosh¹ 

[1] Department of Physics, Visva-Bharati University, Santiniketan 731 235, India$$

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

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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.

【 授权许可】

Unknown