PROOFS PROGRAMME

cm/que/10001 Problem

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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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