29 Oct
2019
29 Oct
'19
8:18 a.m.
On 2019, Oct 18, at 6:04 PM, Ken Thompson via TUHS
<tuhs(a)minnie.tuhs.org> wrote:
while writing "space travel,"
i could not get the space ship integration
around a planet to keep from either gaining or
losing energy due to floating point errors.
i asked dick hamming if he could help. after
a couple hours, he came back with a formula.
i tried it and it worked perfectly. it was some
weird simple double integration that self
corrected for fp round off. as near as i can
ascertain, the formula was never published
and no one i have asked (including me) has
been able to recreate it.
i look forward to the OCR of the code.
I think this must be a variant of “Symplectic Integration”.
My son had an internship at Mitre having something to do with orbit
determination and I got to reading papers about it.
Symplectic integration is what you want for systems described by a Hamiltonian,
such as orbits because the usual integrators (Euler, Runge-Kutta) don’t conserve
the interchange between position and momentum, or something like that.
As far as I can tell, this sort of stuff started getting published in the 1980s,
so Hamming may well have tossed it off earlier and just not written it up.
Could be a nice historical footnote for the development of orbit calculations.
Could be fun to reverse engineer the code.
-L