I have one generalised coordinate, since i can find the x and y intercepts of the ladder from alone.
We have two kinetic energies for this motion, namely
=Translational kinetic energy of the centre of mass along the curve s, and = Rotational kinetic energy of the ladder's rotation about it's centre of mass, with the final kinetic energy given by
Now the potential is is the y component of the centre of mass of the ladder,and
Thus and the lagrangian is given by
Hope this (if correct) can help others.
Prof Lesame, my student number is 36025909