nonrotation

Nonrotation is the state of having zero angular velocity, so an object's orientation does not change with time relative to an inertial or distant-star background. An entity can be nonrotating while still undergoing translation through space; rotation concerns changes in orientation, not position.

In rigid-body dynamics, if the angular velocity vector ω equals zero, the rotation matrix describing the body's orientation is constant. The body’s orientation is fixed in time, meaning it does not spin about its own axis. While ω = 0 implies no spin about the body's center of mass, the object may still carry translational momentum relative to an external origin, which can contribute to orbital angular momentum about that origin.

Nonrotation also appears in the study of reference frames. A non-rotating frame is one whose axes do not rotate relative to distant stars or to a chosen inertial standard; such frames are used to simplify dynamics and to define inertial forces. In general relativity and differential geometry, non-rotating frames are associated with specific transport properties, such as Fermi–Walker transport, which preserves the orientation of a gyroscope along its worldline.

Practical considerations include attitude control in spacecraft, where a vessel is made non-rotating or maintained at a fixed orientation with respect to an inertial frame using thrusters or reaction wheels. In everyday physics, the concept is often illustrated by gyroscopes or by the behavior of a freely falling body in a frame that is momentarily non-rotating.

See also: angular velocity, angular momentum, attitude, inertial frame, gyroscope, non-accelerating frame.