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The tennis racket theorem or intermediate axis theorem, is a kinetic phenomenon of classical mechanics which describes the movement of a rigid body with three distinct principal moments of inertia. It has also been dubbed the Dzhanibekov effect , after Soviet cosmonaut Vladimir Dzhanibekov , who noticed one of the theorem's logical consequences ...
In 1985 he demonstrated stable and unstable rotation of a T-handle nut from the orbit, subsequently named the Dzhanibekov effect. The effect had been long known from the tennis racket theorem, which says that rotation about an object's intermediate principal axis is unstable while in free fall. In 1985 he was promoted to the rank of major ...
The following other wikis use this file: Usage on ar.wikipedia.org مبرهنة مضرب التنس; Usage on de.wikipedia.org Dschanibekow-Effekt
As described in the tennis racket theorem, rotation of an object around its first or third principal axis is stable, while rotation around its second principal axis (or intermediate axis) is not. The motion is simplified in the case of an axisymmetric body, in which the moment of inertia is the same about two of the principal axes.
ANF is a canonical form, which means that two logically equivalent formulas will convert to the same ANF, easily showing whether two formulas are equivalent for automated theorem proving. Unlike other normal forms, it can be represented as a simple list of lists of variable names— conjunctive and disjunctive normal forms also require ...
The first Frenet-Serret formula holds by the definition of the normal N and the curvature κ, and the third Frenet-Serret formula holds by the definition of the torsion τ. Thus what is needed is to show the second Frenet-Serret formula. Since T, N, B are orthogonal unit vectors with B = T × N, one also has T = N × B and N = B × T.
In Riemannian geometry and pseudo-Riemannian geometry, the Gauss–Codazzi equations (also called the Gauss–Codazzi–Weingarten-Mainardi equations or Gauss–Peterson–Codazzi formulas [1]) are fundamental formulas that link together the induced metric and second fundamental form of a submanifold of (or immersion into) a Riemannian or pseudo-Riemannian manifold.
The principle yields an equivalent problem for a radiation problem by introducing an imaginary closed surface and fictitious surface current densities.It is an extension of Huygens–Fresnel principle, which describes each point on a wavefront as a spherical wave source.