Given a smooth bar of mass $M$ and of length $L$ attached to the ceiling in a horizontal position and given a point of mass $m$ on the bar placed in the point of attachment of the bar, find the equations of motion of the point while it is sliding on the bar. At the end of the motion, the point stops at the end of the bar.
The coordinates are the angle $\varphi(t)$ between the bar and the ceiling and $r(t)$ which stands for the distance between the point of attachment and the given point. Initial conditions: $\varphi(0)=\dot{\varphi}(0)=r(0)=\dot{r}(0)=0$.
My equations are:
$$2r\dot{r}\dot{\varphi}+r^2\ddot{\varphi}-(9.81r+ML/2m)\cos\varphi=0$$ $$\ddot{r}-r\dot{\varphi}-9.81\sin\varphi=0.$$
There must appear some motion with dissipation as the massive point on the bar forces it to get the vertical position, however, Wolfram Mathematica gives a different answer, where the point goes to infinity somehow.
I consider a possibility of a mistake because of following: our given point affects the momentum of inertia of the bar. Then, my equations are different from the real ones. Is my consideration correct?