I am making a simulation of $N$-Particles in a cartesian plane and need help with understanding the basics.
At anytime, in my particle system, I will have $N$ number of particles. I am treating the particles as bodies with some radius $r \in (0, 20]$ and giving them properties constrained in a $X \times Y$ unit squared area of a finite plane. Following are the properties a particle can have:
- Mass (Initially supplied)
- Radius (Initially supplied)
- Position (Initially supplied)
- Velocity (Initially supplied)
- Accelaration (when one body attracts another, dynamically generated by the simulator)
Given all this info, I want to make the particle system autonomous, meaning at $t=0$, $N$ particles are laid out on the plane in random locations. At $t>0$, all these particles interact with each other because of the force they exert on each other. I need help understating their fundamental behaviors, especially when can one particle rotate around each other (just like moon does around the earth)? I do understand this concept a little, but what kind of physical and mathematical concepts can help me with this? If possible can you point me to the right web resource pertaining to this matter so I can read about it?