# Intermediate Axis Theorem

Also known as Tennis Racket Theorem.

The tennis racket theorem or intermediate axis theorem is a result in classical mechanics describing the movement of a rigid body with three distinct principal moments of inertia. It is also dubbed the Dzhanibekov effect, after Russian cosmonaut Vladimir Dzhanibekov who discovered the theorem's consequences while in space in 1985. An article explaining the effect was published in 1991.

The theorem describes the following effect: rotation of an object around its first and third principal axes is stable, while rotation around its second principal axis (or intermediate axis) is not.

This can be demonstrated with the following experiment: hold a tennis racket at its handle, with face horizontal, and try to throw it in the air so that it will perform a full rotation around the horizontal axis perpendicular to the handle, and try to catch the handle. In almost all cases, during that rotation the face will also have completed a half rotation, so that the other face is now up. By contrast, it is easy to throw the racket so that it will rotate around the handle axis (the third principal axis) without accompanying half-rotation around another axis; it is also possible to make it rotate around the vertical axis perpendicular to the handle (the first principal axis) without any accompanying half-rotation.

The experiment can be performed with any object that has three different moments of inertia, for instance with a book, remote control or smartphone. The effect occurs whenever the axis of rotation differs slightly from the object's second principal axis; air resistance or gravity are not necessary.

axis
axis of gravity
axis of rotation
concept in inertia
Figure 10.03 - Zero Planes of Depolar Inertia
Figure 12.07 - Plane of Inertia showing Focalizing Action
Figure 12.08 - Plane of Inertia shown as an Optical or Focalizing Function
Figure 3.24 - Non-synchronized Voiding at Plane of Inertia is Regenerative
Figure 5.11 - Dynamics and Development of Circulating Contractive Ring on One Axis
Figure 6.2 - Opposing Repellant Dispersive Radiations Neutralizing at Interface Plane of Inertia
Figure 7.2 - Step 2 - Vortex Formation about a Single Axis
Inertia
inertial plane
Motion-in-inertia
non-motion-in-inertia
Plane of Inertia
triple inertia planes
wave axis
wobbling axis
3.7 - Non-synchronized Voiding at Plane of Inertia