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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 .
Rotation (angular displacement) of a planar figure around a point Rotational orbit v spin Relations between rotation axis, plane of orbit and axial tilt (for Earth) Mathematically, a rotation is a rigid body movement which, unlike a translation, keeps at least one point fixed. This definition applies to rotations in two dimensions (in a plane ...
Each plane through the rotation centre O is the axis-plane of a commutative subgroup isomorphic to SO(2). All these subgroups are mutually conjugate in SO(4). Each pair of completely orthogonal planes through O is the pair of invariant planes of a commutative subgroup of SO(4) isomorphic to SO(2) × SO(2).
A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L 1.Then reflect P′ to its image P′′ on the other side of line L 2.
In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length. There are four types: translations , rotations , reflections , and glide reflections (see below § Classification ).
A rotation represented by an Euler axis and angle. In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point.
Changing orientation of a rigid body is the same as rotating the axes of a reference frame attached to it.. In geometry, the orientation, attitude, bearing, direction, or angular position of an object – such as a line, plane or rigid body – is part of the description of how it is placed in the space it occupies. [1]
The equatorial plane is the plane perpendicular to the axis of rotation of the central body. An inclination of 30° could also be described using an angle of 150°. The convention is that the normal orbit is prograde , an orbit in the same direction as the planet rotates.