where is a generating function, for a contact transformation. This is a partial differential equations in variables for a generating function of a canonical transformation. The solution is denoted by S and is known as Hamilton's principal function.
Contact Transformation, Generating Function, Hamilton's Principal Function
Zwillinger, D. "Hamilton-Jacobi Theory." §10 in Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, pp. 43-45, 1997.
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