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Learn how to rotate a Cartesian coordinate system by an angle and transform the coordinates of points and curves. See examples, formulas, and applications of rotation of axes in two dimensions.
A rotation matrix is a transformation matrix that performs a rotation in Euclidean space. Learn about the definition, properties, examples, and applications of rotation matrices in two and three dimensions.
Rotation is the circular movement of an object around a central line, called an axis of rotation. Learn about different types of rotation, such as spin, revolution, and principal rotations, and how to calculate rotation angle and axis using matrices.
Learn how to represent rotations and reflections in the plane as matrices and how they are related to each other. See examples, identities, and group properties of these Euclidean plane isometries.
Learn about the kinematics and dynamics of rotational motion around a single axis, which is analogous to linear motion along a single direction. Find definitions, formulas, examples, and applications of angular displacement, velocity, acceleration, torque, and moment of inertia.
Learn about the rotation of Earth around its own axis, changes in the orientation of the rotation axis, and the history of the idea of a rotating Earth. Find out how Earth's rotation affects the length of a day, the seasons, the tides, and the shape of the planet.
The right-hand rule is a convention and a mnemonic for various topics in mathematics and physics, such as cross product, magnetic force, coordinate system, and rotation. Learn the history, examples, and variations of the right-hand rule from this Wikipedia article.
The angle θ and axis unit vector e define a rotation, concisely represented by the rotation vector θe.. In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the ...