The problem statement : A uniform ladder of mass m and length 2a rests with one end on a smooth horizontal floor and the other end against a smooth vertical wall.The ladder is initially at rest and makes an angle with the horizontal. Determine the lagrangian function for the ladder. If you see my attached picture,the centre of mass follows a circular path of radius a. I want to use the angle as my generalised coordinate,since i believe the ladders position is completely described by this angle..is this right? Can i use this angle as my generalised coordinate ? Now if L=T-U, can i approximate the motion of the ladder as the motion of it's centre of mass along the circular path s, i.e. T= or will the kinetic energy of the ladder have some rotational components ? What might my kinetic energy equation look like if i allowed for rotation?

So that my lagrangian ( without thinking about rotation and rotational inertias) is given by ... [ s=a and ] and so T=
and U=

so that

L

=

[edit] well it seems i'm slowly solving this one on my own ! Will put what i figure out on here, but just went through my first year mechanics book,seems the kinetic energy is best described by the translational+rotational kinetic energies,where rotational kinetic energy is given by 1/2I

where i is the rotational innertia about the centre of mass of the ladder... back soon