Interesting problem on Lagrangian formalism

[wrobel]

Here is another interesting problem. A planar rigid body of mass $m$ moves in a plane. Let $S$ denote the center of mass of the body. Let us fix a point $A$ in the body such that $|AS| = b > 0$. Let $J$ denote the moment of inertia of the body about the axis passing through point $S$ perpendicular to the plane. An ideal constraint $(\boldsymbol v_A, \boldsymbol Q) = 0$ is imposed on the system. Here $\boldsymbol Q\ne 0$ a vector fixed in the plane. There are no active forces. Write down the equations of motion of the system and integrate them if possible.

 

[wrobel]

I apologize, I didn't realize right away that the constraint is holonomic, so the problem isn't of any interest.