Spatial acceleration


In physics the study of rigid body motion provides for several ways of defining the acceleration state of a rigid body. The classical definition of acceleration entails following a single particle/point along the rigid body and observing its changes of velocity. In this article the notion of spatial acceleration is explored, which entails looking at a fixed point in space and observing the changes of velocity of whatever particle/point happens to coincide with the observation point. This is similar to the acceleration definition fluid dynamics where typically one can measure velocity and/or accelerations on a fixed locate inside a testing apparatus.

Definition

Consider a moving rigid body and the velocity of a particle/point P along the body being a function of the position and velocity of a center particle/point C and the angular velocity.
The linear velocity vector at P is expressed in terms of the velocity vector at C as:
where is the angular velocity vector.
The material acceleration at P is:
where is the angular acceleration vector.
The spatial acceleration at P is expressed in terms of the spatial acceleration at C as:
which is similar to the velocity transformation above.
In general the spatial acceleration of a particle point P that is moving with linear velocity is derived from the material acceleration at P as: