We have battled with the inertia tensor, finding principal axes to make the inertia tensor diagonal. There have been simple JavaScript simulations of rotation at constant speed, but how does a spinning body behave when it is not constrained? How can we simulate something like a tossed coin or a spinning domino? The Euler equations give the answer. There is a proof given here of Euler's equations, but you can really just take them on trust. They tell you that if the principal moments of inertia are all different, the equations become non-linear. The rate-of-change of each component of the angular velocity will depend on the product of the other two. Solving such equations is very difficult indeed, but setting up a simulation to represent them is no problem at all, as you can see in the simulation of the ‘dancing T-handle’. If two of the principal moments are equal, everything becomes much simpler. One of the rates-of-change becomes zero, so the angular velocity about that axis is constant and the equations become linear once again. That describes the case of the gyroscope, where its spin is assumed to remain constant (even though it will actually slow down unless powered). We can add in any couple that is applied to it and get equations for its precession. But the gyroscope has a chapter all to itself.