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Mathematically, the principal axis theorem is a generalization of the method of completing the square from elementary algebra. In linear algebra and functional analysis, the principal axis theorem is a geometrical counterpart of the spectral theorem. It has applications to the statistics of principal components analysis and the singular value ...
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 dubbed the Dzhanibekov effect , after Soviet cosmonaut Vladimir Dzhanibekov , who noticed one of the theorem's logical consequences ...
Matrix representation of conic sections. In mathematics, the matrix representation of conic sections permits the tools of linear algebra to be used in the study of conic sections. It provides easy ways to calculate a conic section's axis, vertices, tangents and the pole and polar relationship between points and lines of the plane determined by ...
In geometry, two conic sections are called confocal if they have the same foci. Because ellipses and hyperbolas have two foci, there are confocal ellipses, confocal hyperbolas and confocal mixtures of ellipses and hyperbolas. In the mixture of confocal ellipses and hyperbolas, any ellipse intersects any hyperbola orthogonally (at right angles).
Poinsot's ellipsoid. In classical mechanics, Poinsot's construction (after Louis Poinsot) is a geometrical method for visualizing the torque-free motion of a rotating rigid body, that is, the motion of a rigid body on which no external forces are acting. This motion has four constants: the kinetic energy of the body and the three components of ...
Spherical version of Malfatti's problem: [4] The triangle is a spherical one. Essential tools for investigations on circles are the radical axis of two circles and the radical center of three circles. The power diagram of a set of circles divides the plane into regions within which the circle minimizing the power is constant.
The result is the parallel axis theorem, = [], where is the vector from the center of mass to the reference point . Note on the minus sign : By using the skew symmetric matrix of position vectors relative to the reference point, the inertia matrix of each particle has the form − m [ r ] 2 {\displaystyle -m\left[\mathbf {r} \right]^{2 ...
Word problem (mathematics) Decision problem pertaining to equivalence of expressions. In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.