The Dzhanibekov effect, 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. Russian cosmonaut Vladimir Dzhanibekov 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.

https://en.wikipedia.org/wiki/Tennis_racket_theorem

https://www.youtube.com/watch?v=1VPfZ_XzisU&feature=emb_rel_end

Ian said:

The Dzhanibekov effect, 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. Russian cosmonaut Vladimir Dzhanibekov 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.

https://en.wikipedia.org/wiki/Tennis_racket_theorem

https://www.youtube.com/watch?v=1VPfZ_XzisU&feature=emb_rel_end

Thank’s Ian.

I would like to say that I’ve heard of this before, but I haven’t.
That rotation about the intermediate axis is unstable is no surprise at all, but I hadn’t seen a proof of it.

As for the other two axes being stable, I’m not 100% sold on that. Some objects, such as Pluto’s small moons, tumble chaotically.
https://www.npr.org/sections/thetwo-way/2015/06/04/411946929/plutos-moons-are-tumbling-in-absolute-chaos-nasa-says . Hyperion, the moon of Saturn, has a chaotic rotation as well. Here is a video of Hyperion’s rotation. https://www.youtube.com/watch?v=tk8r85lM3SY

But then looking at the video of Dzhanibekov, that could be called a weird tumbling motion as well. It resembles the motion of a tippy top, but the physical mechniasm is different.

The video is a ‘must watch’, for those who haven’t already seen it.

Very nice. Thanks.

mollwollfumble said:

Ian said:

The Dzhanibekov effect, 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. Russian cosmonaut Vladimir Dzhanibekov 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.

https://en.wikipedia.org/wiki/Tennis_racket_theorem

https://www.youtube.com/watch?v=1VPfZ_XzisU&feature=emb_rel_end

Thank’s Ian.

I would like to say that I’ve heard of this before, but I haven’t.
That rotation about the intermediate axis is unstable is no surprise at all, but I hadn’t seen a proof of it.

As for the other two axes being stable, I’m not 100% sold on that. Some objects, such as Pluto’s small moons, tumble chaotically.
https://www.npr.org/sections/thetwo-way/2015/06/04/411946929/plutos-moons-are-tumbling-in-absolute-chaos-nasa-says . Hyperion, the moon of Saturn, has a chaotic rotation as well. Here is a video of Hyperion’s rotation. https://www.youtube.com/watch?v=tk8r85lM3SY

But then looking at the video of Dzhanibekov, that could be called a weird tumbling motion as well. It resembles the motion of a tippy top, but the physical mechniasm is different.

The video is a ‘must watch’, for those who haven’t already seen it.

https://www.npr.org/sections/thetwo-way/2015/06/04/411946929/plutos-moons-are-tumbling-in-absolute-chaos-nasa-says

This shows near spherical objects. Any Dzhanibekov effect is going to be hard to observe.

The YouTube I posted points out that some asteroids are tumbling in an apparently chaotic way, but that they demonstrate the effect regardless.