Rotation Dynamics of a Rigid Body with Vector Calculus and Geometric Algebra
Channel: Tony the Taiwanese Turtle
Date: 2021-09-30

In this video we we will first review intermediate dynamics; we will go through the derivation of the covariant time derivative in a rotating moving frame, and then we will use the results from the derivation to further derive the relations between angular momentum, rotational inertia, and torque. Then we will go through the same topics as in the first, but with geometric algebra. And finally in the last part of the video, I will summarize and compare the two results.

Content correction:
Starting from 14:44, for the grade 2 component of the geometric product [H][Omega_theta], I mistakenly added a dot in between the two bivectors. Ironically (in the context of the No - Yes meme I used), the conventional notation for the grade 2 component of the geometric product of two bivectors turns out to be the cross product symbol (see wikipedia page for bivector: https://en.wikipedia.org/wiki/Bivector#Product_of_two_bivectors ).

Parts of the Video:
00:00 Introduction

Part 1 Review of Intermediate Dynamics with Vector Calculus
00:59 1-1 Time Derivative in a Rotating Moving Frame
05:01 1-2 Angular Momentum, Rotational Inertia, and Torque

Part 2 Deriving the Same Results with Geometric Algebra
08:15 2-1 Time Derivative in a Rotating Moving Frame
10:46 2-2 Angular Momentum, Rotational Inertia, and Torque

14:58 Summary and Compare

Contents of this video can also be found in this article: 
https://twnturtletony.medium.com/9f88e812633a

The background music used in the title slides is "Light Sting" by Kevin MacLeod. It was found on YouTube Audio Library.