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{\bf SOLUTIONS FINAL ADVANCED DYNAMICS\\~\\ PHY 4241 (Spring, 2011)}\\ 
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\centerline{\bf PROBLEM 1}\bigskip

See Homework 9 and $L(q_i+\epsilon_i,\dot{q}_i,t)=L(q_i,\dot{q}_i,t)$
implies
$$ 0 = \frac{\partial L}{\partial q_i} = \frac{d~}{dt}\,
   \frac{\partial L}{\partial \dot{q}_i}\ \Rightarrow\  
   p_i = \frac{\partial L}{\partial \dot{q}_i}\ {\rm conserved\
   (generalized\ momentum).} $$
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