Interaction and movement

We know movement should be part of the classical mechanical description because changes in the movement state of objects are part of our everyday lives. How can we accommodate the concept in our theory?
First, we recognize that a universe with a single particle cannot present movement states for the particle. Therefore, the movement must be a property of a system of two or more particles. If we have a universe with two particles, we must allow the particles to interact, in this case, to change their respective states of movement. In the real world, we know by experiment that two particles with values of mass do interact by gravitation. We also know that two particles with electric charge interact by electric and magnetic fields.
A single particle that does not interact with any other particle is a free particle. Ideally, we may have a system of two or more free particles, i.e., particles that form a mechanical system but do not interact with each other, but this would be a very uninteresting system. We may have a system with several particles that interact among themselves but do not interact with other particles or systems; in this case, we call this a closed system, or an isolated system.
We may always separate a system of particles, and form sub-systems, by using a definite criterium. For example, a system with \(n\in\mathbb{N}\) particles, each with a mass \(m_1\), and another system with \(k\in\mathbb{N}\) particles, each with a mass \(m_2\), may be seen as two sub-systems of a larger system with \(n+k\) particles with distinct masses. In this case, a system with \(n\) particles may always be seen as \(n\) systems, each with a single particle.