From: henry@spsystems.net
In article <420a2ed8$0$70247$ed2619ec@ptn-nntp-reader03.plus.net>,
Ian Stirling wrote:
>With the advent of PCs that can do hundreds of millions, or billions
>of calculations per second at high precision, simply ignoring all of this
>fancy calculus stuff, and calculating forces acting on the spacecraft, and
>the resultant accellerations and positions, every minute, for a decade long
>mission is not a big problem.
However, doing it millions of times, in an attempt to *optimize* that
trajectory, remains a big problem. The fancy stuff comes in when you are
trying to find an optimal flight plan in reasonable amounts of time,
rather than just calculating the results for a pre-chosen flight plan.
Even today, brute force has its limits.
In fact, there has never been a good alternative to raw number crunching
for calculating the results of a realistic low-thrust flight plan. The
analytical results are too limited to be of a lot of use, except for a
few stereotyped problems like slow transitions between circular orbits.
Especially when you start figuring in various perturbing forces that
the analytical models can't handle.
The serious math comes back in the door for optimization work.
>You of course need to pay attention to errors and rounding.
Indeed. Which means, in fact, that typically you don't *want* to do that
calculation for every minute of a decade-long mission. You want numerical
methods that are good enough to let you take fewer and longer steps, to
reduce the inherent accumulation of roundoff error. (In fact, typically
you want automatic step-size control, using step methods which estimate
their own errors to guide step-size choice.)
--
"Think outside the box -- the box isn't our friend." | Henry Spencer
-- George Herbert | henry@spsystems.net
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