0

I am doing a project with the fundamental background not in my major. I am reading the following lecture:

enter image description here

How to get the green part?

Can anyone show me the detailed derivation or provide the note for reference?

(There might be similar questions; however I only want the specific derivation or explanation of some steps not the last result.)

sleeve chen
  • 233
  • 1
    The detailed derivation of the first expression can be found in the book Classical Mechanics by Herbert Goldstein in the chapter "The Kinematics of Rigid Body Motion". The second expression is obtained after applying the small angle approximation to $\cos\delta\theta$ and $\sin\delta\theta$, i.e., $\cos\delta\theta\approx 1$ and $\sin\delta\theta\approx\delta\theta$. – Procyon May 09 '16 at 03:03
  • Also related: http://physics.stackexchange.com/questions/103895/rotating-reference-frames , http://physics.stackexchange.com/questions/135210/time-derivative-of-angular-velocity-in-rotating-reference-frame , and many others. – David Hammen May 09 '16 at 05:13
  • 1
    Rotation of a vector :
    http://physics.stackexchange.com/questions/252942/rotation-of-a-vector/253390#253390

    Velocity in a turning reference frame : http://physics.stackexchange.com/questions/67053/velocity-in-a-turning-reference-frame/252265#252265

     – Frobenius May 09 '16 at 18:53
  • Thank @Frobenius That link solves my problem. I mark my problem duplicate. – sleeve chen May 09 '16 at 21:33

1 Answers1

2
John Alexiou
  • 38,341
  • 1
    Unless you remember the name it is difficult to search for it. Best guess would be to search for "Rotation About Arbitrary Axis". – John Alexiou May 09 '16 at 13:43