HCR - Representation of Forces on the Reference Frame

Every force on an object can be represented in the object RF (Reference Frame) usually defined as its barycenter by another Force plus a Torque.

Also every interaction the object has with the world can be summarized by an external Force and an external Moment (or Torque)

• To compute the Torque ${\tau }^{\prime }$

in the RF (reference frame) $0$ →

$${\left(\begin{array}{l}{M}_{x_0}\\ M_{y_0}\\ M_{z_0}\end{array}\right)}_0={\overrightarrow{b}}_0\wedge {\overrightarrow{F}}_0$$

• The vector product can be computed using the Skew Matrix: