Description
Every solid body inherently has three principal axes through its center of mass, and each of these axes has a corresponding moment of inertia. The moment of inertia about an axis is a measurement of how difficult it is to accelerate the body about that axis. The closer the concentration of mass to the axis, the smaller the torque required to get it spinning at the same rate about that axis.
The moment of inertia of a body depends on the mass distribution of the body and on the arbitrarily selected axis about which the moment of inertia is defined. The moments of inertia about two of the principal axes are the maximum and minimum moments of inertia of the body about any axis. The third is perpendicular to the other two and has a moment of inertia somewhere between the maximum and minimum.
If energy is dissipated while an object is rotating, this will cause the polhode motion about the axis of maximum inertia (also called the major principal axis) to damp out or stabilize, with the polhode path becoming a smaller and smaller ellipse or circle, closing in on the axis.
A body is never stable when spinning about the intermediate principal axis, and dissipated energy will cause the polhode to start migrating to the object’s axis of maximum inertia. The transition point between two stable axes of rotation is called the separatrix along which the angular velocity passes through the axis of intermediate inertia.
Rotation about the axis of minimum inertia (also called the minor principal axis) is also stable, but given enough time, any perturbations due to energy dissipation or torques would cause the polhode path to expand, in larger and larger ellipses or circles, and eventually migrate through the separatrix and its axis of intermediate inertia to its axis of maximum inertia.
It is important to note that these changes in the orientation of the body as it spins may not be due to external torques, but rather result from energy dissipated internally as the body is spinning. Even if angular momentum is conserved (no external torques), internal energy can be dissipated during rotation if the body is not perfectly rigid, and any rotating body will continue to change its orientation until it has stabilized around its axis of maximum inertia, where the amount of energy corresponding to its angular momentum is least.
Read more about this topic: Polhode
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