Hamilton's principal function

The Hamilton's principal function is defined by the Hamilton Jacobi equation (HJE), another alternative formulation of classical mechanics. This function is related to the usual action, , by fixing the initial time and endpoint and allowing the upper limits and the second endpoint to vary; these variables are the arguments of the function. In other words, the action function is the indefinite integral of the Lagrangian with respect to time.

Klappentext

The Hamilton's principal function is defined by the Hamilton-Jacobi equation (HJE), another alternative formulation of classical mechanics. This function is related to the usual action, , by fixing the initial time and endpoint and allowing the upper limits and the second endpoint to vary; these variables are the arguments of the function. In other words, the action function is the indefinite integral of the Lagrangian with respect to time.