Proofing Contractive Functions: Difficulties Solved • Physics Forums

KF33 · 2016-06-18T19:33:49+00:00

I am having a hard problem with working on this proof.

Thread 'How does time derivative commute from one variable to another?'

I'm reviewing Meirovitch's "Methods of Analytical Dynamics," and I don't understand the commutation of the derivative from r to dr: $$ \mathbf{F} \cdot d\mathbf{r} = m \ddot{\mathbf{r}} \cdot d\mathbf{r} = m\mathbf{\dot{r}} \cdot d\mathbf{\dot{r}} $$

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