SYMMETRIES, NOETHER THEOREM AND INEQUIVALENT LAGRANGIANS APPLIED TO NONCONSERVATIVE SYSTEMS

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.