Motion examples

1. Translation \[\vec{x}' = \vec{x}+\vec{t}\]
2. Rotation \[\vec{x}' = \vec{x}\cdot R\]
   • But note that \(R\) is not an arbitrary matrix.
   • We’ll return to the restrictions

Definition: Rigid Body Motion

1. 3D Object is a set of points in \(\mathbb{R}^3\)
2. If the object moves, the constituent points move
3. The points have to move so that they preserve the shape of the object