Symmetries and conservation laws of the damped
harmonic oscillator
AMITAVA CHOUDHURI, SUBRATA GHOSH and B TALUKDAR*
Department of Physics,
Santiniketan 731 235,
*Corresponding author. E-mail: binoy123@bsnl.in
Abstract. 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.
Keywords. Damped harmonic oscillator; explicitly
time-dependent
Lagrangian representation; Noether symmetries;
conservation laws.
PACS Nos 45.20.Jj; 45.20.df; 45.20.dh