Acceleration Transformation Rules
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To find
the acceleration transformation rules recall
The
acceleration in the primed coordinates may be obtained by finding the
differential of Eq. (1) and then utilizing
Thus we
start by taking the differential of Eq. (1a)
This can
be simplified by collecting terms yielding
Dividing
Eq. (3) by the expression for dt’ in Eq. (2) gives the final result
Next
take the differential of Eq. (1b) to obtain
As
above, this can be simplified by collecting terms yielding
Similarly
for the y component
