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 Exercise [20.17] 
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Joined: 12 Jul 2010, 07:44
Posts: 154
Post Exercise [20.17]
The Euler-Lagrange equation states:

\frac{\mbox{d}}{\mbox{d}t}\frac{\partial\mathcal{L}}{\partial\dot{q}^r}=\frac{\partial\mathcal{L}}{\partial q^r}

We define p_r=\frac{\partial\mathcal{L}}{\partial\dot{q}^r}

When \mathcal{L} is independent of q^r, the right-hand side of the Euler-Lagrange equation is zero, and so we get:

\frac{\mbox{d}}{\mbox{d}t}p_r=0

...i.e. p_r is a conserved quantity.

\blacksquare


19 May 2012, 09:01
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