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two-dimensional mechanics

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Pasha Zusmanovich

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Jul 30, 2009, 11:11:13 AM7/30/09
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Dear people,

I am wondering whether there exists an accurate description of the
Newtonian mechanics, and, in particular, the treatment of the N-body
problem, in the (plane) 2-dimensional world.

Cheers, Pasha.

enders

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Aug 1, 2009, 7:51:00 AM8/1/09
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Hello Pasha,

It seems to me that the chapters 'Definitions' and 'The Laws of
Motions' in the 'Principia' are independent of whether they are
considered for 3D or for 2D.

Newton's force law can be deduced from the corresponding Poisson
equation (which in turn can be deduced - in case of interest I could
send you my papers about how), thus, in 2D, the potential varies as ln
(1/r). If the corresponding N body problem is non-integrable - as it
is in 3D - I don't know, but I would guess so.

BTW, 2D effects, when compared with 3D behaviour, are observable in
very thin layers of solids, eg, in semiconductor lasers.

Best wishes,
Peter

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