Proof Validity: Self-Reflection & Textbook Support

Jimmy Chung · 2013-08-22T20:58:29+00:00

is this proof valid? I thought it out myself with some help from textbooks?

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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