Newton's laws

The motions of bodies are based on three laws that were experimentally verified by Newton and should hold in any inertial frame:

1. An object at rest tends to stay at rest, and an object in motion tends to stay in motion with fixed speed, unless a nonzero resultant^13.8force acts upon it.
2. The relationship between a body mass $m$, its acceleration $a$, and an applied force $f$ is $f = ma$.
3. The interaction forces between two bodies are of equal magnitude and in opposite directions.

Based on these laws, the differential constraints on a system of moving bodies can be modeled.