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Subsections

quaternion time derivative

Syntax

Quaternion   dot(const ColumnVector & w, const short sign)const;
ReturnMatrix E(const short sign)const;

Description

The quaternion time derivative is obtain from the quaternion propagation law [2].
$\displaystyle \dot{s}$ $\textstyle =$ $\displaystyle -\frac{1}{2}v^Tw$ (2.22)
$\displaystyle \dot{v}$ $\textstyle =$ $\displaystyle \frac{1}{2}E(s,v)w$ (2.23)

where
$\displaystyle \begin{array}{cc}
E = \eta I - S(\epsilon) & \textrm{in base frame} \\
E = \eta I + S(\epsilon) & \textrm{in body frame}
\end{array}$     (2.24)

The choice of reference system (base or body) for $ w $ is assign by $ sign $. A value of $1$ is for base frame while $-1$ is for body frame.

Return Value

Quaternion for dot

Matrix for E



Richard Gourdeau 2004-07-06