A multi-body system is a system that has two or more independantly moving bodies under consideration. Each body has a mass, distributed about some center of mass, and an inertia around the center of mass.

*For the purpose of this post, only the 2D case of a robotic arm with a linear actuator will be considered.*

# Representing Positions

For representation of the positions, the points of interest can be defined in either global or local reference frames.

**Insert Picture**

In the above figure, the global reference frame origin is denoted as $o_0$ and the local reference frames origins are denoted as $o_1$, $o_2$. The respecitve x and y axes are accordingly denoted as $x_0$, $x_1$, $x_2$ and $y_0$, $y_1$, $y_2$.