Three phenomena impact these calculations:
These are not orthogonal.
With small enough Δt and enough precision the chaos
would not cause trouble.
Chaos matters when we want to know the outcome of
the infinitely precise initial conditions.
This is not a pratical issue.
- Rounding (finite precision of the hardware floating point,
including the confusion of variable scaling which entails variable significance.)
- Truncation (finite value of Δt)
In this note I will quantify precision as significant bits.
32 bit IEEE floatingpoint format (float in C) provides 24 significant bits
and 64 bit format (double) provides 53.
The extended precision of the Pentium provides 64 significant bits using
the C construct “long double”.
Chaos increases the sensitivity of the calculation to
initial conditions more than for two body problems.
I have not yet gained evidence that we have computed to
the encounter that indeed expels a lone mass.
Chaos together with either truncation or rounding make ...
are met except upon mass collision.
This ensures that almost all initial conditions yield exactly one solution.
See Picard’s Theorem.
I have code to compute the Lyaopnov coefficient.