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# Problem/CM-10001 Canonical Transformations

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The motion of a particle undergoing constant acceleration $$a$$ in one dimension is described by
\begin{eqnarray*}
x &=& x_0 + \frac{p_0t}{m} + \frac{1}{2}a t^2\\
p&=&p_0+m a t
\end{eqnarray*}Show that the transformation from the present old'' varaibles $$(x,p)$$ to initial new'' variables $$(x_0,p_0)$$ is a canonical transformation

(a) by Poisson bracket test
(b) by finding ( for $$t\ne0$$ ) the type 1 generaging function $$F_1(x,x_0,t)$$

Source:Calkin

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