Show me a derivation of the BKE

[abercrombiems02]

For any of you advanced dynamics people, can you please show me a derivation of the BKE. (Basic Kinematic Equation)

The BKE is...

e d/dt(Vector) = u d/dt(Vector) + omega between e and u X (Vector)

sometimes an additional term is added which is the linear velocity between the frames but for some simplicity let's assume this is zero.

e is the inertial frame
and u is the working frame

omega is the angular velocity
X is the cross product operator

I know just by looking at a simple single rotation problem, the solution is trivial but does anyone know of a formal proof?

 

[FredGarvin]

I do, but I think it will take me a month of Sundays to write here. Let me see if I can scan in my old dynamics notes from school. Give me a bit!

 

[abercrombiems02]

Thanks, take your time, I'm in no rush!

 

[FredGarvin]

Here we go. I had to scan it in from my Dynamics class notes. The pdf is a bit rough on the quality side. If you can't read it, let me know and I'll e-mail you the scan.

 

[abercrombiems02]

thanks alot! This works perfectly. I actually found a more geometrical way to prove it with the few extra hours i had to spare today. Unfortunately, I don't have a scanner to show anyone to ensure correctness. Perhaps when I get back to school I can scan it in and have someone verify that my method is correct. Thanks again!