HCR - Pose of a Rigid Body

A rigid body is completely described in a reference frame by position and orientation. The position of point $O{}^{\prime }$ on the rigid body with respect to the coordinate frame $O$ ($x,y,z$) is expressed by a three dimensional vector $<o{}_x^{\prime },o{}_y^{\prime },o{}_z^{\prime }>$.

Where $o{}_x^{\prime },o{}_y^{\prime },o{}_z^{\prime }$ are versors. (??? it doesn't make sense, they should not be versors ???NOT_SURE_ABOUT_THIS )

So the position of $O{}^{\prime }$ with respect to $O$ is defined as:

$$O{}^{\prime }=o{}_x^{\prime }+o{}_y^{\prime }+o{}_z^{\prime }$$

In this case:

• $O$ : is the World reference frame
• $O{}^{\prime }$ : is the Object reference frame

The idea is: I want to know $O{}^{\prime }$ in respect to $O$. This because in my system $O$ is NOT allowed to change (being the world reference frame) so it’s perfect for referencing $O{}^{\prime }$ that can change.

While for the position of $O{}^{\prime }$ with respect to $O$, we can use the position of each vector of the object frame with respect to the reference frame: We obtain a representation of rotation by the Rotation Matrix