Newton's Laws of Motion

Newton's laws of motion, in the rather obscure language of the Principia, take the following form:

1. Every body continues in its state of rest, or uniform motion in a straight-line, unless compelled to change that state by forces impressed upon it.
2. The change of motion (i.e., momentum) of an object is proportional to the force impressed upon it, and is made in the direction of the straight-line in which the force is impressed.
3. To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal and directed to contrary parts.

Let us now examine how these laws can be applied to dynamical systems.