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ON THE STABILITY PROBLEM FOR THE
FREE RIGID BODYPreview AbstractIn the general case of the
free rigid body, we will give a list of integrals of motion, which generate the set of Mishchenko's integrals. In the case of 
, we prove that there are 15 coordinate-type Cartan subalgebras which on a regular adjoint orbit give 15 Weyl group orbits of equilibria. These coordinate-type Cartan subalgebras are the analogs of the three axes of equilibria for the classical rigid body on 
. The nonlinear stability and instability of these equilibria is analyzed. In addition to these equilibria there are 10 other continuous families of equilibria.