Saturday 29 August 2015

newtonian mechanics - Time derivative of angular velocity in rotating reference frame


I am going through a section in a textbook regarding the Newton Euler equations for a system of rigid bodies (robotics text). There is a particular line in the derivation I don't understand, I've attached the image to make it clear:



enter image description here


I think the derivative of the second term on the right-hand side of 3.28 is using the product rule to get to 3.32, but I don't understand where the cross-product comes from. Could someone explain this particular part of the derivation? Thanks.



Answer



It is worth it for you reading about differentiating vectors on rotating frames.



Appendix


In addition, to prove equation (3.28) follow this answer https://physics.stackexchange.com/a/65768/392 or https://physics.stackexchange.com/a/105099/392


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