Canonical Transformations & Hamilton-Jacobi Method (Math Heavy) - Goldstein Ch 9, 10

In this video, we learn how to transform between canonical coordinate bases using canonical transformations. Then we learn the Hamilton-Jacobi method of solving physical problems by transforming coordinates to constants. 0:00 Canonical Transformations 8:55 Hamilton-Jacobi Method Textbook: Goldstein, Herbert, et al. Classical Mechanics. 3rd ed., Pearson Education Inc., 2002. Plot generated by Wolfram|Alpha: https://www.wolframalpha.com/input?i=... Classical Mechanics playlist:    • Let's Learn Physics   Tutor site: https://www.physicstutorchris.com/ Author Site: https://www.christiandhorst.com Patreon:   / christiandhorst   Buy Me A Coffee: https://www.buymeacoffee.com/christia... #Physics #ClassicalMechanics #CanonicalTransformations