Online tutor?

On Oct 28, 2:29*am, Martin Brown
wrote:
On 27/10/2012 10:16, Andy Walker wrote:









On 26/10/12 23:38, Dr J R Stockton wrote:
[...] It's not just "common" opinion; *eg, Kopal's
"Close Binary Systems" says explicitly [p546] "The five point-
solutions were discovered by J. L. Lagrange in his 'Essai [...]
(cf his /Collected Works/, *6*, p.229)," *Kopal was a meticulous
researcher with access to a huge library and would certainly have
read the /Essai/, so I'm surprised he got it wrong.
Well, if that's an accurate quote, he did not know how Lagrange's
initials are usually written. [...] *But, IIRC, his tomb
does lack the hyphen.

* * *Back in the '50s, there was less concern about historical
consistency. *But ZK must have read the /Essai/, and must have
checked to find the page number, so it's surprising that he got
the discovery wrong. *My other usual source on celestial mechanics,
Roy's "Orbital Motion" is much more circumspect, and seems to
agree with you about the history. *You're right, BTW, that the
tomb lacks the hyphen.

I remember Prof Kopal he was one of the people who got me interested in
astronomy as a youngster. He was patron of the local astrosoc and did an
annual lecture.

The relevant chapters of the Essay contain no instances of the word or
number five. *Read it yourself - it's quite an easy read, if the actual
maths is disregarded.

* * *It's quite an easy read with the maths included! *But I'm
v happy to take your word for it.

I think that it taking things a little bit too literally. Lagrange
derived the always an equilateral triangle stable solution for the three
body problem independently as a part of his rediscovery of the Euler
solutions of 1767 which he published in 1772.

I am paraphrasing from Celestial Encounters - another book on the
history of orbital dynamics discoveries. Its referencing is not that hot
but based on dates I think the book to be checked is
Lagrange, J.L, Oeurves, vol 6, p272-292 Paris 1873

He almost certainly didn't call them L4, L5 (later authors did).

I did find a copy from 1873 online athttp://gallica.bnf.fr/ark:/12148/bpt6k229225j/f294.image.r=Oeuvres%20...

You want page 292 under the heading XXXIII. He did know about the pure
equilateral planar solution at least in his French writings.

It would be necessary to work back through the references chain to see
whether later authors were rewriting history here or just clarifying
things that Lagrange had actually said in earlier Latin papers.

My assessment of the book as a whole is that it could use a few more
diagrams and a lot less turgid French prose! YMMV

Regards,
Martin Brown

I have this wonderful magazine in front of me from 1983,it is the
Discover Magazine's 'Year in Science' and it is such a wonderful read -
there are adds for whiskey and cigarettes,vhs tapes and vinyl records
and dotted between are stories which now look really dated -nuclear
winter,acid rain and those trial balloons until they hit the jackpot
a decade later with 'climate change' nee,global warming where everyone
got implicated in destroying the planet or rather infested with the
belief that humans can control the planet's temperature

Among those articles is a wonderful essay about Langrangians,now this
was written at a time when people could actually reason and there is a
sense of dismay,almost inevitability about the whole thing as
mathematicians drift further and further away from common sense that
most people call reality.I am taking the time out to post the relevant
passage in that essay as it is not available online,not so much to
expose the 30 year lament but rather its prescience -

"A Langrangian is not a physical thing;it is a mathematical thing - a
kind of differential equation to be exact.But physics and maths are so
closely connected these days that it is hard to separate the numbers
from the things they describe.In fact,a month after [Philip]
Morrison's remarks,Nobel Prize winner Burton Richter of the Stanford
Linear Accelerator Center said something that eerily echoed it: "
Mathematics is a language that is used to describe nature" he said
"But the theorists are beginning to think it is nature.To them the
Langrangians are the reality " Discover 1983

A people enveloped in their own imagination and using a language they
understand among themselves are hardly the people who would stop to
look at the geometrical language of astronomy and the extraordinary
and one-off event where a conclusion was reached using an extension of
the 24 hour AM/PM system and the Lat/Long system by inserting an
explanation for planetary dynamics using right ascension when it is
impossible.In this case mathematics do not substitute for reality but
affirm it as a reasonable,if not sane ,person can safely affirm that
all their experiences within a 24 hour cycle reflect one rotation of
the Earth and they never,ever fall out of step.Long before
Langrangians there was Ra/Dec,a system on which Newton built his
absolute/relative time,space and motion agenda and the mathematicians
in the late 17th and following centuries never stopped to consider
whether the clockwork solar system arising from the Ra/Dec system
reflected reality - it doesn't.