The Slipping Ladder Problem with Friction

We model the ladder as a rigid body and assume constant friction at the contacts. After setting up the equation of motion, a nonlinear ordinary differential equation, we derive the analytical solution as position-dependent velocity, i.e. the angular velocity as a function of the angle. By evaluating a numerical example, we observe that the presented model is not yet fully realistic, as the normal contact force at the wall can become negative, which requires switching to a nonsmooth mechanics model. Intended as educational material for courses in applied mechanics or classical physics, this exercise bridges the gap between introductory textbook statics and advanced non-linear dynamics.