Spatial Acceleration

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 (unmoving) 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.

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Spatial Acceleration - Definition
... 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 In general the spatial acceleration of a particle point P that is moving with linear velocity is derived from ...
Rigid Body - Kinematical Equations - Other Quantities
... the origin of a local coordinate system L, attached to the body, the spatial or twist acceleration of a rigid body is defined as the spatial acceleration of C (as opposed to material acceleration above) where ... of the rigid body represents the total velocity of the point/particle represents the total acceleration of the point/particle represents the angular acceleration ... the spatial acceleration of the origin of L) In 2D the angular velocity is a scalar, and matrix A(t) simply represents a rotation in the xy-plane by an ...