Page 9d -- 3d Global Positions as a Function of Time Coordinate transformations also provide the opportunity to track a single body through time. Imagine a body positioned at several points along its trajectory. Due to variations in position, velocity, angular rotation, etc., the local coordinate system of the body will change with respect to global at each instant in time. This combination of translations and rotations can be described mathematically, similar to the description of relative motion of two bodies. A transformation matrix can be constructed at each point in time to solve for displacement, rotation about a body axis, accelerations, and other kinematic details.