Abstract
This paper presents the Hamilton-Jacobi method for integrating the equations of motion of mechanical systems on time scales. We give the criterion and four basic forms of canonical transformation on time scales. Also, various examples are given to illustrate the role played by a generating function in the canonical transformation. By choosing an appropriate generating function, we construct the Hamilton-Jacobi equation on time scales and prove the Jacobi theorem on time scales. An example for an Emden-Fowler type equation is discussed to show the application of the method.
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