The Acceleration Vector of a Rigid Body

Abstract

This paper explains the relationship between two existing representations of rigid-body acceleration in a 6-D vector: conventional acceleration, which is the concatenation of two 3-D acceleration vectors, and spatial acceleration, which is the time derivative of a 6-D velocity vector. The two are materially different and obey different composition rules. In particular, spatial accelerations behave like true vectors, and conventional accelerations do not. This paper shows that the conventional acceleration of a rigid body is its apparent spatial acceleration in a moving coordinate system. This implies that both vectors describe the same physical phenomenon but in different coordinate systems. It also implies that rigid-body acceleration really is a vector. The paper concludes with some examples showing how 6-D accelerations are used.