Integration Unsolvable Problem

A rotating, solid body that is simulated on a computer is done by calculating each frame after a miniscule amount of time.

I believe that it is possible to predict the actual frame of orientation of a rotating body with a high degree of accuracy by using theorectical equations. Well, as far as I know, there is no solution for a theorectical equation. I am trying to find one where the property of a roating body can be calculated after any given amount of time.

I am trying to solve this equation at the moment. It describes the propety of a rotating body against time.

where I __believe__ that

where F is a function of time for a periodic waveform and all instances of k are different constants. Eg *F* could be sin(kt) but a simply sine function does not satisfy the differential.

Anyone knows of any solutions!