Search results
Results from the WOW.Com Content Network
Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.
The angular displacement (symbol θ, ϑ, or φ) – also called angle of rotation, rotational displacement, or rotary displacement – of a physical body is the angle (in units of radians, degrees, turns, etc.) through which the body rotates (revolves or spins) around a centre or axis of rotation.
These rotations form the special orthogonal group SO(m), the group of m × m orthogonal matrices with determinant 1. For m = 3 this is the rotation group SO(3) . In another definition of the word, the rotation group of an object is the symmetry group within E + ( n ) , the group of direct isometries ; in other words, the intersection of the ...
A sphere rotating (spinning) about an axis. Rotation or rotational motion is the circular movement of an object around a central line, known as an axis of rotation.A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation.
In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .
3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]
The rotation axis is sometimes called the Euler axis. The axis–angle representation is predicated on Euler's rotation theorem, which dictates that any rotation or sequence of rotations of a rigid body in a three-dimensional space is equivalent to a pure rotation about a single fixed axis. It is one of many rotation formalisms in three dimensions.
Rotational frequency, also known as rotational speed or rate of rotation (symbols ν, lowercase Greek nu, and also n), is the frequency of rotation of an object around an axis. Its SI unit is the reciprocal seconds (s −1 ); other common units of measurement include the hertz (Hz), cycles per second (cps), and revolutions per minute (rpm).