We prove that the classical, non-periodic Toda lattice is super-integrable. In other words, we show that it possesses 2N-1 independent constants of motion, where N is the number of degrees of freedom. The main ingredient of the proof is the use of some special action-angle coordinates introduced...

The Dirac brackets approach to description of the dynamics of dynamical systems in presence of the phase-space constraints is illustrated here on few examples taken from classical and continuum mechanics course.