Timeline for What is the relation between the different generating functions thought as finite approximations of action functionals
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| May 2, 2019 at 13:39 | comment | added | BrianT | Thanks. Where do you see a similar construction as Chaperon's in these notes ? | |
| May 2, 2019 at 12:48 | comment | added | Nawaf Bou-Rabee | This relationship is discussed in Section 1.4.4 of Discrete Mechanics and Variational Integrators cds.caltech.edu/~marsden/bib/2001/09-MaWe2001/MaWe2001.pdf Note that generating functions can be expressed in any local coordinate system and specifically any two of $q_0$, $p_0$, $q_1$ and $p_1$, and each pair leads to generating functions of different types. The most common choice is probably $q_0$ and $q_1$ (pair of configurations), and in this case, the relation between the generating function and the action is given by Jacobi's solution to the Hamilton-Jacobi PDE in (1.7.1). | |
| May 2, 2019 at 11:43 | history | asked | BrianT | CC BY-SA 4.0 |