We know that the origin of a coordinate system is arbitrary. For example, when we have a problem  to find the position of a falling object (constant acceleration), we can always say that it started at y=0. We define our coordinate system properly, but as long as we are consistent, we will get the correct answer.

 

We can also define the start time arbitrarily. We say initially T=0.

 

The initial orientation of the system is also arbitrary.

 

We have the following quantities that we must specify:

 

Initial time

Initial position. In three dimensions, we specify the initial x,y, and z.

Initial orientation. We have three angles to specify.

 

By coincidence, there are various quantities that are conserved:

 

Energy

Momentum (three components)

Angular momentum (three components)