Two bodies with the same mass, m, are connected with a massless rope through a small hole in a
smooth horizontal plane. One body is moving on the plane, the other one is hanging at the end of the
rope and can move vertically. At all instances the rope is tight. The acceleration due to gravity is g.
a) Find the Lagrange’s equations of motion in polar coordinates (r; ) and explain their physical
meaning. Discuss special cases.
b) Reduce the equations of motion to a one dimensional problem in r with an effective potential
and discuss the motion