Rotation

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A rotation is a circular movement of an object around a center (or point) of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation about an external point, e.g. the Earth about the Sun, is called a revolution or orbital revolution, typically when it is produced by gravity.

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Mathematics

Mathematically, a rotation is a rigid body movement which, unlike a translation, keeps a point fixed. This definition applies to rotations within both two and three dimensions (in a plane and in space, respectively.)

All rigid body movements are rotations, translations, or combinations of the two.

A rotation is simply a progressive radial orientation to a common point. That common point lies within the axis of that motion. The axis is 90 degrees perpendicular to the plane of the motion. If the axis of the rotation lay external of the body in question then the body is said to orbit. There is no fundamental difference between a “rotation” and a “orbit” and or "spin". The key distinction is simply where the axis of the rotation lay, either within or without a body in question. This distinction is and can be demonstrated in and for both “ridged” and “non ridged” bodies.

If a rotation around a point or axis is followed by a second rotation around the same point/axis, a third rotation results. The reverse (inverse) of a rotation is also a rotation. Thus, the rotations around a point/axis form a group. However, a rotation around a point or axis and a rotation around a different point/axis may result in something other than a rotation, e.g. a translation.

Rotations around the x, y and z axes are called principal rotations. Rotation around any axis can be performed by taking a rotation around the x axis, followed by a rotation around the y axis, and followed by a rotation around the z axis. That is to say, any spatial rotation can be decomposed into a combination of principal rotations.

In flight dynamics, the principal rotations are known as yaw, pitch, and roll (known as Tait-Bryan angles). This terminology is also used in computer graphics.

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