Na. Lemos, SYMMETRIES, NOETHER THEOREM AND INEQUIVALENT LAGRANGIANS APPLIED TO NONCONSERVATIVE SYSTEMS, Revista Mexicana de Fisica, 39(2), 1993, pp. 304-313
Symmetry properties, Noether's theorem and inequivalent Lagrangians ar
e discussed and applied to simple one-dimensional nonconservative syst
ems. In the most elementary instances, the standard constants of the m
otion combined with other conserved quantities associated with previou
sly overlooked spacetime symmetries of the action lead to a complete a
lgebraic solution of the equations of motion. In the more difficult ca
se of the damped harmonic oscillator, two inequivalent Lagrangians are
employed. Noether invariances of the corresponding actions are identi
fied by inspection, allowing the determination of two independent cons
tants of the motion from which the general solution to the equation of
motion is algebraically found.