| 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. |
