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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 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.
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.
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body.
Exact time integration of the above formula from time = to time = + yields the exact update formula: + = + (((, + /)) ((, /))). Godunov's method replaces the time integral of each ∫ t n t n + 1 f ( q ( t , x i − 1 / 2 ) ) d t {\displaystyle \int _{t^{n}}^{t^{n+1}}f(q(t,x_{i-1/2}))\,dt} with a forward Euler method which yields a fully ...
Whenever a theory is decidable, and the language of its valid formulas is countable, it is possible to extend the theory with countably many relations to have quantifier elimination (for example, one can introduce, for each formula of the theory, a relation symbol that relates the free variables of the formula). [citation needed]
The Chebychev–Grübler–Kutzbach criterion determines the number of degrees of freedom of a kinematic chain, that is, a coupling of rigid bodies by means of mechanical constraints. [1]