Janibekov Effect
The Dschanibekow effect , also known as the tennis racket effect , is a special form of staggering a force-free rotating body that was observed in 1985 by the Soviet cosmonaut Vladimir Dschanibekow on a wing nut during a space flight . See also the adjacent video, which shows the effect on a handle .
Basically it has been known since 1834 that a freely rotating body with three different main moments of inertia only shows a stable orientation of the axis of rotation when it rotates approximately around one of the two main axes of inertia , to which the largest or smallest moment of inertia belongs. When rotating around the third, perpendicular main axis of inertia, on the other hand, the body develops large staggering movements from the smallest deviations if the angular momentum vector does not initially coincide exactly with this main axis of inertia . The angular momentum vector itself remains constant, but not the direction of the momentary axis of rotation in relation to the body-fixed and spatial coordinate system.
The particularly peculiar kind of staggering that Dschanibekow observed in weightlessness even seems to include a repeated reversal of the direction of rotation (as seen in the video). However, this reversal only applies to the body-fixed coordinate system, while the direction of rotation is not reversed when viewed from the spatially fixed system .
This movement was theoretically founded in 1991. From a mathematical point of view, the effect is based on the fact that the relevant main axis of inertia on the energy ellipsoid does not belong to an elliptical, like the other two axes, but to a hyperbolic fixed point (more precisely: to a saddle point ); For more information, see Movement of force-free tops .
See also
- Poinsot construction (third animation in the introduction of the article)
literature
- Léo Van Damme, Pavao Mardesic, Dominique Sugny: The tennis racket effect in a three-dimensional rigid body. Arxiv , 2016.
Individual evidence
- ↑ yavideleto: Джанибеков ( Dschanibekow ) on YouTube, February 19, 2010, accessed June 29, 2019 (in Russian). TV interview in which cosmonaut Vladimir Dzhanibekov explains the effect to a journalist.
- ^ Louis Poinsot : Théorie nouvelle de la rotation des corps. Bachelier, Paris 1834/1851
- ↑ Mark S. Ashbaugh, Carmen C. Chicone, Richard H. Cushman: The twisting tennis racket. In: Journal of Dynamics and Differential Equations , 3, 1, 1991, pp. 67-85.