Alan C
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 Dec 25 comment Meaning of a canonical transformation “preserving” a differential form? Thanks. So for $n=1$, we would need $\frac{\partial P}{\partial p} \frac{\partial Q}{\partial q} - \frac{\partial P}{\partial q} \frac{\partial Q}{\partial p} = 1$? Dec 25 asked Meaning of a canonical transformation “preserving” a differential form? Nov 1 accepted How to explain the different forms of the Hamilton-Jacobi equation? Nov 1 comment How to explain the different forms of the Hamilton-Jacobi equation? Thank you for your help! Nov 1 comment How to explain the different forms of the Hamilton-Jacobi equation? What do you mean by depending explicitly on $t$? Is there a way for it to depend implicitly on $t$? And does this have to do with the fact that Arnold's definition of canonical requires that $H(q, p, t) = K(Q, P, t)$? (since this would imply that $K - H \equiv 0$. Nov 1 comment How to explain the different forms of the Hamilton-Jacobi equation? The way I understand it, the unknown in both PDEs is the generating function. Does the $K$ somehow turn into $-\partial S_2 / \partial t$ if you switch from type 1 to type 2? Nov 1 awarded Editor Nov 1 revised How to explain the different forms of the Hamilton-Jacobi equation? added 4 characters in body Nov 1 asked How to explain the different forms of the Hamilton-Jacobi equation? Aug 22 awarded Scholar Aug 22 accepted Conservation of angular momentum across different reference frames? Aug 22 comment Conservation of angular momentum across different reference frames? Thank you for the explanations! Aug 18 awarded Supporter Aug 18 comment Conservation of angular momentum across different reference frames? Thanks for your answer! I have some questions: (1) When you say "you don't take into account usual $g$," what exactly do you mean? In gyroscopes, for example, the gravity produces a torque which causes a change in angular momentum. (2) Where does the term $L_0$ come from? I thought changing $J$ to $J+mv$ would account for the change in reference frame. Aug 17 awarded Student Aug 14 asked Conservation of angular momentum across different reference frames?