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Let's say for simplicity that the particle is uniaxial and the torque is applied somewhere on its axis (but not in the center). The coordinates of the particle are the position of the center of mass (R) and an orientation unit vector (u). We know that the rotational kinetic energy is given in terms of the angular velocity of the body (w) as wIw/2, where I is the moment of inertia, not in terms of the conjugate momenum of the coordinates u, while the potential energy is a function of u. The relation between the orientation and angular velocity is:

(du/dt)=w x u.

I would like to know which set of coordinates and conjugate momenta would you use to solve such a problem?

Thank you in advance for any help :).