Table 1.

The notations used in this paper.

Notation Rules
x	Scalar
x	Vector
X	Matrix
x̄ (or X̄)	Transpose of x (or X)
x̃ (or X̃)	Conjugate of x (or X)
Kinematic Variables
sAB	Position vector of point A with respect to point B
${\upsilon }_{\mathrm{A}}^{\text{I}}$	Velocity vector of point A with respect to frame I
$a_{\mathrm{A}}^{\text{I}}$	Acceleration vector of point A with respect to frame I
ωEI	Rotational speed vector of frame E with respect to frame I
qEI	Quaternion expressing the rotation of frame E with respect to frame I
Coordinate Systems
[sAB]E	Position vector sAB expressed in the coordinate system E
{qEI}E	Quaternion with its vector part expressed in the coordinate system E
[T]EI	Transition matrix from coordinate system I to coordinate system E