Curvilinear Coordinates, part 2: Mechanics (Kepler's Problem and Euler's Three-Body Problem)

Previous episode https://www.youtube.com/live/u53bvqNA... 0:00:00 - 0:17:50 Overview and plan 0:17:50 - 0:24:00 (Canadian) Thanksgiving prayer 0:24:00 - 1:00:00 Review of curvilinear coordinates, tangent vectors, Lamé coefficients 1:00:00 - 1:24:00 Velocity formula 1:24:00 - 1:40:00 Example: polar coordinates 1:40:00 - 4:19:30 Acceleration formula, multiple digressions: debunking AI-doomerism, textbook choice 4:19:30 - 4:30:00 Example: cylindrical coordinates 4:30:00 - 4:39:30 Check the acceleration formula using the free Lagrangian 4:39:30 - 6:47:31 Kepler’s problem: deriving Kepler’s Three Laws 6:47:31 - 7:25:00 Kepler’s problem: time dependence and Kepler’s equation 7:25:00 - 8:24:35 Euler’s two-centre problem: applications of elliptic coordinates Reference. Vector and Tensor Analysis with Applications, by A. I. Borisenko and I. E. Tarapov