Equation of Motion on a Rotating Sphere Using Lagrangian Mechanics
Channel: Tony the Taiwanese Turtle
Date: 2022-04-28

In this video we derive the equation of motion of a point mass or a continuum on a rotating sphere in spherical coordinates using Lagrangian mechanics. This version of the equation of motion is well-fit for describing the point motion or fluid physics on Earth.

Parts of the VIdeo:
00:00 0. Entry Theme
00:07 1. Introduction
00:44 2. Why Using Newtonian Mechanics is Difficult
01:51 3. Equation of Motion of Point Mass
01:57 4. Notations in This Video
02:29 5. Velocity Components
03:30 6. Kinetic Energy
04:32 7. Euler-Lagrangian Equations
05:27 8. Terms in the Euler-Lagrangian Equations
09:35 9. Equation of Motion in Terms of Force, Velocity, and Acceleration
12:16 10. Coriolis Effect and Centrifugal Effect
13:22 11. Equation of Motion of Continuum
13:44 12. Assumptions for Simplification
14:35 13. Resulting EOM for Continuum

Software used for making this video:
- Audacity was used for eliminating the white noises of the recordings
- Blender was used for video editing
- Microsoft Powerpoint was used for making the slides