Circular velocity and acceleration with geometric algebra
Peeter's math and physics play
In this video, the geometric algebra form for the circular unit vectors will be derived, and then used to compute expressions for velocity and acceleration in a circular coordinate system.
This video includes a very brief introduction to (2D) geometric algebra, including the exponential form for a 2D rotation. Specifically, this video includes:
- A reminder of what circular coordinates are.
- A brief outline of what is meant by each of the circular basis vectors.
- A derivation of those basis vectors (just basic geometry, and no GA.)
- A brief introduction to geometric algebra, and geometric algebra for a plane, including the "imaginary" i = e_1 e_2, and it's use for rotation and polar form.
- How to express the circular basis vectors in polar form.
- Application of all the ideas above to compute velocity and acceleration.
- Circular coordinate examples of velocity and acceleration.
Prerequisites: calculus (derivatives and chain rule), complex numbers (exponential polar form), and basic vector algebra (basis, vector space, dot product space, arrow representation of vectors, graphical vector addition, ...)
If you liked this material you may be interested in my blog:
or my book (Geometric Algebra for Electrical Engineers), which is available for free in pdf form at:
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