Search results
Results from the WOW.Com Content Network
The parallel axis theorem, also known as Huygens–Steiner theorem, or just as Steiner's theorem, [1] named after Christiaan Huygens and Jakob Steiner, can be used to determine the moment of inertia or the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of gravity and the perpendicular distance between ...
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 ...
Parovicenko's theorem ; Parallel axis theorem ; Parseval's theorem (Fourier analysis) Parthasarathy's theorem (game theory) Pascal's theorem ; Pasch's theorem (order theory) Peano existence theorem (ordinary differential equations) Peeling theorem ; Peetre theorem (functional analysis) Peixoto's theorem (dynamical systems)
When calculating moments of inertia, it is useful to remember that it is an additive function and exploit the parallel axis and perpendicular axis theorems. This article mainly considers symmetric mass distributions, with constant density throughout the object, and the axis of rotation is taken to be through the center of mass unless otherwise ...
In classical mechanics, the stretch rule (sometimes referred to as Routh's rule) states that the moment of inertia of a rigid object is unchanged when the object is stretched parallel to an axis of rotation that is a principal axis, provided that the distribution of mass remains unchanged except in the direction parallel to the axis. [1]
Where the planar second moment of area describes an object's resistance to deflection when subjected to a force applied to a plane parallel to the central axis, the polar second moment of area describes an object's resistance to deflection when subjected to a moment applied in a plane perpendicular to the object's central axis (i.e. parallel to ...
The proofs given in this article use these definitions, and thus apply to non-negative angles not greater than a right angle. For greater and negative angles , see Trigonometric functions . Other definitions, and therefore other proofs are based on the Taylor series of sine and cosine , or on the differential equation f ″ + f = 0 ...
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 ...