Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe...

known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space...

express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular)...

In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector...

Mathematically, a rotation is a rigid body movement which, unlike a translation, keeps at least one point fixed. This definition applies to rotations...

Rotation operator may refer to: An operator that specifies a rotation (mathematics) Three-dimensional rotation operator Rot (operator) aka Curl, a differential...

In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention...

rotation around a fixed axis of a rigid body are mathematically much simpler than those for free rotation of a rigid body; they are entirely analogous to...

In mathematics and physics, vector is a term that refers informally to some quantities that cannot be expressed by a single number (a scalar), or to elements...

Bunch, Bryan H. (1982). Mathematical Fallacies and Paradoxes. Van Nostrand Reinhold. pp. 10–11. ISBN 0-442-24905-5. "Rotational dynamics - Center of wheel...

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...

Earth's rotation or Earth's spin is the rotation of planet Earth around its own axis, as well as changes in the orientation of the rotation axis in space...

may also refer to: Rotation (anatomy) Rotation (mathematics) Rotation (medicine), medical student training Rotation (physics), ratio between a given angle...

In mathematics, the rotation number is an invariant of homeomorphisms of the circle. It was first defined by Henri Poincaré in 1885, in relation to the...

In discrete mathematics, tree rotation is an operation on a binary tree that changes the structure without interfering with the order of the elements....

mathematics, a function defined on an inner product space is said to have rotational invariance if its value does not change when arbitrary rotations...

Crop rotation is the practice of growing a series of different types of crops in the same area across a sequence of growing seasons. This practice reduces...

In mathematics, the group of rotations about a fixed point in four-dimensional Euclidean space is denoted SO(4). The name comes from the fact that it...

two rotations results in another rotation, every rotation has a unique inverse rotation, and the identity map satisfies the definition of a rotation. Owing...

Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world...

to a reflection. The statements above can be expressed more mathematically. Let a rotation about the origin O by an angle θ be denoted as Rot(θ). Let a...

or "number of cycles") is formalized as a dimensionless quantity called rotation, defined as the ratio of a given angle and a full turn. It is represented...

infinitesimal rotation matrix or differential rotation matrix is a matrix representing an infinitely small rotation. While a rotation matrix is an orthogonal...

recognized for his development of quaternions, a mathematical system for representing three-dimensional rotations, is often attributed with the introduction...

Look up torsion in Wiktionary, the free dictionary. Torsion may refer to: Torsion (mechanics), the twisting of an object due to an applied torque Torsion...

In mathematics, a group is a set with an operation that satisfies the following constraints: the operation is associative and has an identity element...

composition of rotations chained rotations. The geometrical definition demonstrates that three composed elemental rotations (rotations about the axes...

In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating...

In geometry, an improper rotation (also called rotation-reflection, rotoreflection, rotary reflection, or rotoinversion) is an isometry in Euclidean space...

angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity...