We indicated in the last chapter that the calculus of variations provides an alternative characterization of the motion of mass particles in the form of Hamilton’s principle. Often the variational characterization is actually more effective for determining the motion of a dynamical system. For many problems, use of particle trajectories in Cartesian coordinates is not efficient for the solution process. For the particular example to be analyzed below, it is more advantageous to use cylindrical polar coordinates. For other problems, the primary dependent variables may not even be length or geometrical quantities. In the next few sections, we will show how the equations of motion in non-Cartesian (or generalized) coordinates can be obtained very efficiently with the help of the calculus of variations.