Page 464 - Introduction to Continuum Mechanics

448 Integral Formulation of General Principles

Since

thus,

i.e.,

But, from a course in rigid body dynamics, we learned that for any vector b.

Where a> is the angular velocity of ¥2 relative to F\. Thus,

Therefore,

Now, the linear momentum relative to F\ is J v/r dm and that relative to p2 is Jv/r dm.
These rates of change of linear momentum are related in the following way: (for simplicity,
we drop the subscript of the integral V m )

Now, again, using Eq. (iii) for the vector J v/r dm, we have