Angular Momentum Constraint
In the absence of applied torques, the angular momentum vector is conserved in an inertial reference frame .
The angular momentum vector can be expressed in terms of the moment of inertia tensor and the angular velocity vector
which leads to the equation
Since the dot product of and is constant, and itself is constant, the angular velocity vector has a constant component in the direction of the angular momentum vector . This imposes a second constraint on the vector ; in absolute space, it must lie on an invariable plane defined by its dot product with the conserved vector . The normal vector to the invariable plane is aligned with . The path traced out by the angular velocity vector on the invariable plane is called the herpolhode (coined from Greek roots for "serpentine pole path").
Read more about this topic: Poinsot's Ellipsoid
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