Jacques Philippe Marie Binet showed that the angular momentum vector lies on the intersection of a sphere and an ellipsoid. The angular velocity along the principal axis of a freely rotating rigid body is described by Euler's equations from the point of view of an observer rotating with the body, a motion known as nutation (as in the case of a top). The angular velocity vector is a constant of motion viewed from the body system.
Euler's equations take the form of the autonomous system
 R. Kent Nagle, E. B. Saff, A. D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, 6th ed., Boston: Pearson Addison-Wesley, 2012 pp. 275–276.
 H. Goldstein, Classical Mechanics, 2nd ed., Reading, MA: Addison-Wesley, 1980.