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Mon, 28 Oct 2019 22:18:47 -0400 (EDT) Content-Type: text/plain; charset=utf-8 Mime-Version: 1.0 (Mac OS X Mail 12.4 \(3445.104.11\)) From: Lawrence Stewart In-Reply-To: Date: Mon, 28 Oct 2019 22:18:46 -0400 Content-Transfer-Encoding: quoted-printable Message-Id: <363F5ECC-7F3E-4441-B9E7-2828BF21F303@serissa.com> References: <201910181152.x9IBq95P001809@coolidge.cs.Dartmouth.EDU> <20191018183610.diq_a%steffen@sdaoden.eu> To: The Eunuchs Hysterical Society X-Mailer: Apple Mail (2.3445.104.11) Subject: Re: [TUHS] Space Travel, was New: The Earliest UNIX Code X-BeenThere: tuhs@minnie.tuhs.org X-Mailman-Version: 2.1.26 Precedence: list List-Id: The Unix Heritage Society mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: tuhs-bounces@minnie.tuhs.org Sender: "TUHS" > On 2019, Oct 18, at 6:04 PM, Ken Thompson via TUHS = wrote: >=20 > 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. >=20 > i look forward to the OCR of the code. >=20 I think this must be a variant of =E2=80=9CSymplectic Integration=E2=80=9D= . My son had an internship at Mitre having something to do with orbit=20 determination and I got to reading papers about it. Symplectic integration is what you want for systems described by a = Hamiltonian,=20 such as orbits because the usual integrators (Euler, Runge-Kutta) = don=E2=80=99t conserve=20 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,=20 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