14 questions linked to/from Hamilton-Jacobi Equation
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### Intuition for Hamilton-Jacobi equation derived from least action

I am trying to understand the Hamilton-Jacobi equation without the framework of the canonical transformations. Even on the case of a 1D free particle I'm getting stuck. The system starts at fixed ...
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### Geometry of Hamilton-Jacobi Equation

I'm trying to understand the geometry of the Hamilton-Jacobi equation (working from Gelfand + Fomin), but I'm stuck. I know that: If we define the function $S(t,y;t_0, y_0)$ as: S(t,y;t_0,y_0) = \...
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### Is this action a Hamilton's principal function?

In Ref. 1, in section 3, they wrote: \begin{equation} L'(q,\dot{q},\ddot{q},t)~=~L(q,\dot{q},\ddot{q},t)-\frac{dS(q,\dot{q},t)}{dt}.\tag{14} \end{equation} Then the Hamilton-Jacobi equation is \begin{...
I am having some trouble with understanding why it makes sense to consider action in classical mechanics as function of endpoints $q_{initial}, \ q_{final}$ and endtimes $t_{initial}, \ t_{final}$. ...