A rigid body system is an assembly of different parts which are joints, rigid bodies and forces. A joint connects two different bodies and gather all kinematic relations between those two bodies, allowing the creation of a relative displacement between the two bodies. This displacement is described by breaking it down into three parts, rotations, translations or the compositions of a rotation and a translation.

Rotation matrices form the so-called **Special Orthogonal** group \f$ SO-n) \f$. There are two groups within the latter which interest us as for now: \f$ SO(2) \f$ and \f$ SO(3) \f$. \f$ SO(3) \f$ is the group of all rotations in the 3-dimensionnal space. Its elements are matrices of size 3 by 3. \f$ SO(3) \f$ is useful for planar problems. It is the group of rotations in the 2-dimensionnal space. Its elements are matrices of size 2 by 2.

Rotation matrices form the so-called **Special Orthogonal** group \f$ SO(n) \f$. There are two groups within the latter which interest us as for now: \f$ SO(2) \f$ and \f$ SO(3) \f$. \f$ SO(3) \f$ is the group of all rotations in the 3-dimensionnal space. Its elements are matrices of size 3 by 3. \f$ SO(3) \f$ is useful for planar problems. It is the group of rotations in the 2-dimensionnal space. Its elements are matrices of size 2 by 2.

The set that brings together all the homogeneous transformations matrices is the **Special Euclidean** group \f$ SE(n) \f$. As with rotation matrices, there are two different groups, \f$ SE(3) \f$ for 3-dimensional transformations and \f$ SE(2) \f$ for 2-dimensional transformation, i.e. transformation in a plane.