page_title: Tennis racket theorem
hierarchical_section_title: Tennis racket theorem
caption_attribution_description: English: Illustration included in Mark S. Ashbaugh, Carmen C. Chicone and Richard H. Cushman (1991). "The Twisting Tennis Racket". Journal of Dynamics and Differential Equations. Article describes the Tennis racket theorem
context_page_description: 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 noticed one of the theorem's logical consequences while in space in 1985 although the effect was already known for at least 150 years before that.
  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 is not.
  This can be demonstrated with the following experiment: hold a tennis racket at its handle, with its face being 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.
context_section_description: 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 noticed one of the theorem's logical consequences while in space in 1985 although the effect was already known for at least 150 years before that.
  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 its face being 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 only slightly from the object's second principal axis; air resistance or gravity are not necessary.
caption: Principal axes of a tennis racket.
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