On 25/10/12 08:44, Martin Brown wrote:
On 24/10/2012 21:14, Dr J R Stockton wrote:
Contrary to common opinion, Lagrange did not discover the Lagrange
Points - although the final step to the Points from what he did is
trivial, he did not take it in the /Essai/, and, AFAICS, nowhere else
either.

Interesting. 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.

[...] Most physics undergraduates today would
struggle to derive the orbital Lagrangian points from first
principles.

This may well be true, esp if they are simply given the
problem with no hints or "signposts". However, the derivation
is not particularly difficult, either for the Lagrange problem
of finding persistent configurations or for the usual restricted
three-body problem, as long as vector algebra is used to keep
the equations simple. I see no reason why a student shouldn't
be able to follow such a derivation, or to construct it given
reasonable pointers as to how to proceed.

The Lagrange points are also very easy to derive from
the Jacobi integral, by either vectorial or algebraic methods.
As this is essentially the potential energy of the system, this
derivation is also accessible to anyone who has done Hamiltonian
or Lagrangian mechanics -- surely still in the physics syllabus
at decent universities, even if not common knowledge among 8yos!
-- and gives scope then for discussion of stability.

--
Andy Walker,
Nottingham.