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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 ...
Japanese theorem for concyclic polygons (Euclidean geometry) Japanese theorem for concyclic quadrilaterals (Euclidean geometry) John ellipsoid ; Jordan curve theorem ; Jordan–Hölder theorem (group theory) Jordan–Schönflies theorem (geometric topology) Jordan–Schur theorem (group theory)
The following other wikis use this file: Usage on ar.wikipedia.org مبرهنة مضرب التنس; Usage on de.wikipedia.org Dschanibekow-Effekt
Theorem [7] — Suppose T is a distribution on U with compact support K. There exists a continuous function f {\displaystyle f} defined on U and a multi-index p such that T = ∂ p f , {\displaystyle T=\partial ^{p}f,} where the derivatives are understood in the sense of distributions.
The classical statement of the Künneth theorem relates the singular homology of two topological spaces X and Y and their product space. In the simplest possible case the relationship is that of a tensor product , but for applications it is very often necessary to apply certain tools of homological algebra to express the answer.
For functions of a single variable, the theorem states that if is a continuously differentiable function with nonzero derivative at the point ; then is injective (or bijective onto the image) in a neighborhood of , the inverse is continuously differentiable near = (), and the derivative of the inverse function at is the reciprocal of the derivative of at : ′ = ′ = ′ (()).
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.