Velocity from position vector in rotating object

1. Jul 26, 2017

Nikstykal

1. The problem statement, all variables and given/known data
I am trying to solve for change in velocity for the center of a rim with respect to the contact patch of a tire that has some degree of camber. The equation finalized is shown in the image below, equation 2.6.
http://imgur.com/a/oHucp

2. Relevant equations

3. The attempt at a solution
I understand how to get the position vector shown in 2.5. The first part of 2.6 is just deriving 2.5 with respect to h. The 3rd and 4th terms are what confuse me. In regards to dj/dt = -wz i, I understand that the change in j with respect to time is directly related to the yaw moment (wz) but what is the mathematical reasoning for using the i unit vector? Further, the 4th term demonstrates that dk/dt = -γ' / cos2 γ j, showing that k = -tanγ.
Sorry for the improper notation, was hoping to get further insight into how these terms are being derived.

Last edited: Jul 26, 2017
2. Jul 26, 2017

Dr.D

I can't see your figure, and without that, there is no good way to reply to you. Please get the figure into the post.

3. Jul 26, 2017

Nikstykal

Sorry about that, should be fixed.