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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 ...
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 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 ...
[1] Some coordinate systems in mathematics behave as if they were real gimbals used to measure the angles, notably Euler angles . For cases of three or fewer nested gimbals, gimbal lock inevitably occurs at some point in the system due to properties of covering spaces .
Sylvester's theorem or Sylvester's formula describes a particular interpretation of the sum of three pairwise distinct vectors of equal length in the context of triangle geometry. It is also referred to as Sylvester's (triangle) problem in literature, when it is given as a problem rather than a theorem.
In electromagnetism, surface equivalence principle or surface equivalence theorem relates an arbitrary current distribution within an imaginary closed surface with an equivalent source on the surface. It is also known as field equivalence principle, [1] Huygens' equivalence principle [2] or simply as the equivalence principle. [3]
By using the change of variables log f ↦ u, another commonly found form of Liouville's equation is obtained: =. Other two forms of the equation, commonly found in the literature, [4] are obtained by using the slight variant 2 log f ↦ u of the previous change of variables and Wirtinger calculus: [5] = ¯ =.
Layer cake representation. In mathematics, the layer cake representation of a non-negative, real-valued measurable function defined on a measure space (,,) is the formula = (,) (),