Re: Variational calculus : A drop of water

On Thu, 16 Apr 2009 02:07:56 -0700 (PDT),
charlescalculus_robertobaggio@xxxxxxxxxxx wrote:

Hi, anyone observed a drop of water before and noticed that while
falling, it is supposed to be spherical?

I know that it is a sphere but I need to prove it using variaional
calculus. Anyone got any hints?

Also, what good book are there on these kind of isoperimetric
problems?

I've got a book by I.M. Gelfand and Fomin, but it doesn't cover this
problem.

http://arxiv.org/abs/chao-dyn/9811020
Simulation of a Dripping Faucet by Nobuko Fuchikami, Shunya Ishioka1
and Ken Kiyono
"A dripping faucet system is simulated. We numerically show that a
hanging drop generally has many equilibrium shapes but only one among
them is stable. By taking a stable equilibrium shape as an initial
state, a simulation of dynamics is done, for which we present a new
algorithm based on Lagrangian description."
"In Appendix A, we describe a variational algorithm to examine
stability of static solutions. Our algorithm of simulation of dynamics
is presented in Appendix B."

Its been a long time since I used this. Good luck!

There was an extensive discussion of the problem on sci.physics
http://groups.google.com/group/sci.physics/browse_thread/thread/83aecebdfb7d6876/ae3477605ebf7a59
.

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