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...

angle θ {\displaystyle \theta } . A rotation of axes in more than two dimensions is defined similarly. A rotation of axes is a linear map and a rigid transformation...

figure at a center of rotation. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary...

coordinates. For example, in two dimensions rotating a body clockwise about a point keeping the axes fixed is equivalent to rotating the axes counterclockwise...

In geometry, there exist various rotation formalisms to express a rotation in three dimensions as a mathematical transformation. In physics, this concept...

an axis running from wing to wing; and roll, rotation about an axis running from nose to tail. The axes are alternatively designated as vertical, lateral...

three-dimensional rotations are parameterized for physics, or medicine, or chemistry, or other disciplines. When we include the option of world axes or body axes, 24...

the 3-fold axes are each through one vertex and the center of one face. Rotational symmetry with respect to any angle is, in two dimensions, circular symmetry...

of rotations (i.e. chained rotations). The geometrical definition demonstrates that three consecutive elemental rotations (rotations about the axes of...

In ballistics and flight dynamics, axes conventions are standardized ways of establishing the location and orientation of coordinate axes for use as a...

In numerical linear algebra, a Givens rotation is a rotation in the plane spanned by two coordinates axes. Givens rotations are named after Wallace Givens...

axis of a composite rotation defined in terms of the axes of the two rotations. He derived this formula in 1840 (see page 408). The three rotation axes A...

In the case of multiple mirror planes and/or axes of rotation, two symmetry groups are of the same symmetry type if and only if there is a rotation mapping...

axis of a composite rotation defined in terms of the axes of the two rotations. He derived this formula in 1840 (see page 408). The three rotation axes A...

case in which first and third axes are overlapping. The general problem of decomposing a rotation into three composed movements about intrinsic axes was...

orienting a rigid body is based upon body-axes rotation; successive rotations three times about the axes of the body's fixed reference frame, thereby...

of rotations associated with simple bivectors in the algebra. Planes of rotation are not used much in two and three dimensions, as in two dimensions there...

In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in...

coordinate axes or just axes (plural of axis) of the system. The point where the axes meet is called the origin and has (0, 0) as coordinates. The axes directions...

corresponding to a set of axes. But in rotational symmetry, there is no reason why one set of axes is preferred to say, the same set of axes which has been rotated...

improper rotation symmetry. In 3 dimensions, improper rotation is equivalently defined as a combination of rotation about an axis and inversion in a point...

generate rotations in four dimensions, much like vectors are used to define rotation axes in three dimensions. In the familiar three-dimensional space of daily...

a single rotation about some axis that runs through the fixed point. It also means that the composition of two rotations is also a rotation. Therefore...

any arbitrary angle and map onto itself. Rotational circular symmetry is isomorphic with the circle group in the complex plane, or the special orthogonal...

into simple mirror planes; Screw axes are converted into simple axes of rotation) Axes of rotation, rotoinversion axes and mirror planes remain unchanged...

In mathematics, the special orthogonal group in three dimensions, otherwise known as the rotation group SO(3), is a naturally occurring example of a manifold...

According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at...

occurs when the axes of two of the gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate two-dimensional space...

identifying the positive direction of coordinate axes in three dimensions. William Rowan Hamilton, recognized for his development of quaternions, a mathematical...

reflection in a plane and a 180° rotation about a line perpendicular to that plane. For n = 2 there is not one main axis and two additional axes, but there...