

\item{(14)} Assume a bilinear kinetic Energy
$$ T = \sum_{j,k} a_{jk}\,\dot{q}_j\dot{q}_k~~{\rm and\ prove}~~
   \sum_i \dot{q}_i\,\frac{\partial T}{\partial\dot{q}_i} = 2T\ .$$

\item{(15a)} Generalized Momentum:
$${\rm Calculate}~\frac{\partial L}{\partial x_i},\
i=1,2,3,~{\rm for}~L=\frac{1}{2}\,m\,\vec{v}^{\,2}-V(\vec{x}).$$
Due January 29 in class (2 points).

