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Classical mechanics discusses the behaviour of macroscopic bodies under the influence of forces (without necessarily specifying the origin of these forces). If it's possible, USE MORE SPECIFIC TAGS like [newtonian-mechanics], [lagrangian-formalism], and [hamiltonian-formalism].

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How to check $\mathbf v' · \mathbf V$ and $\mathbf v'^2$ are time derivatives of some other ...

From Landau, Lifshitz Mechanics p.127 $$ \renewcommand{\vec}[1]{\mathbf{#1}} L'=\frac{1}{2}m(\vec{v}'^2+\vec{v'}\cdot\vec{V}+\vec{V}^2)-U $$ He states that "$\vec{V}^2(t)$ can be written as the tota …
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