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Terminating Motion

Ifwithseparation of variables gives

Ifatwe can integrate this:

Rearrangement gives

This motion is only defined forWhengoes to infinity. Of course in any physical system the model will break down before this time. In general the motion is defined as terminating if it is represented by a solution of the motion which is undefined at some finite time.

If(1) then

which can be arranged to give

The system reachesatNo motion satisfying (1) is possible after this time and the motion terminates there.