The velocity with respect to the centre of mass
![R](/media/stories/equations/classicalmechanics/masspoint01.gif)
![v-R](/media/stories/equations/classicalmechanics/masspoint02.gif)
![coordinates of the centre of mass](/media/stories/equations/classicalmechanics/masspoint03.gif)
In a 2-particle system, the coordinates of the centre of mass are given by:
![coordinates of the centre of mass for 2-particle system](/media/stories/equations/classicalmechanics/masspoint04.gif)
With
![r=r1-r2](/media/stories/equations/classicalmechanics/masspoint05.gif)
![](/media/stories/equations/classicalmechanics/masspoint06.gif)
![](/media/stories/equations/classicalmechanics/masspoint07.gif)
![reduced mass](/media/stories/equations/classicalmechanics/masspoint08.gif)
The motion within and outside the centre of mass can be separated:
![](/media/stories/equations/classicalmechanics/masspoint09.gif)
![](/media/stories/equations/classicalmechanics/masspoint10.gif)
Collisions
With collisions, where B are the coordinates of the collision and C an arbitrary other position, holds:
![](/media/stories/equations/classicalmechanics/masspoint11.gif)
![](/media/stories/equations/classicalmechanics/masspoint12.gif)
![changes in the relative velocities](/media/stories/equations/classicalmechanics/masspoint13.gif)
![](/media/stories/equations/classicalmechanics/masspoint14.gif)
![](/media/stories/equations/classicalmechanics/masspoint15.gif)
![L](/media/stories/equations/classicalmechanics/masspoint16.gif)