Binet's Ellipsoid

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.


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Euler's equations take the form of the autonomous system
[1] 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.
[2] H. Goldstein, Classical Mechanics, 2nd ed., Reading, MA: Addison-Wesley, 1980.
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