In Hamilton Jacobi theory the transformations are time dependent.

Demand

tex2html_wrap96

Set tex2html_wrap97 .

Then tex2html_wrap98 tex2html_wrap99 Which is the Hamilton-Jacobi theory. Solution up to a constant of a nonlinear PDE.

S=solution to Hamilton's principal function= tex2html_wrap100 where tex2html_wrap101 are constants of integration. Treat the tex2html_wrap101 as momentum.

S is coincidentally the action. tex2html_wrap103

tex2html_wrap104 constant so tex2html_wrap105

Sometimes the W's seperate out well.




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