N-body problem

N-body problem is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

wp:N-body problem is a problem of physical description of mechanical system of N interacting objects. System is described by newton's law ${\vec {F}}=m_{i}{\frac {d^{2}{\vec {r}}_{i}}{dt^{2}}},i=1..N$ with continious combined force from other bodies$F_{i}=\sum _{j}F_{ij},i=1..N$.

Exact formulation of first mechanical problem is, given initial coordinates and velocities $t=0$, to find coordinates and velocities at $t=t_{0}$ with accuracy more then given relative value $\epsilon ={\frac {{\vec {r}}-{\vec {r}}'}{|{\vec {r}}|}}$

As well known from physical background, only the choice of N=2 can be analythically solved.