[QUE/ME-130001] ME-PROBLEM

Express the kinetic energy, the linear momentum, and the angular momentum of a system of \(N\) particles in terms of the Jacobi coordinates \begin{eqnarray} \vec{R}_j&=&\frac{m_1\vec{r}_1 + \ldots + m_j \vec{r}_j}{m_1+\ldots+m_j}-\vec{r}_{j+1}, \qquad j=1,\ldots,(N-1).\\ \vec{R}_N &=& \frac{m_1\vec{r}_1 + \ldots + m_N \vec{r}_N}{m_1+\ldots+m_N} \end{eqnarray}
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