Re: Variational calculus : A drop of water

On Apr 16, 2:07 pm, charlescalculus_robertobag...@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.

This can be solved with constraint of given area to maximize volume
using a Lagrange multiplier. Use cylindrical coordinate system and
Euler-Lagrange Equation with two independent variables.

Narasimham

.

Relevant Pages

  • Re: surface area of n-dimensional sphere
    ... of n dimensions and wonder how to approach the problem. ... I'm only looking for hints, ... dimensional sphere. ... with calculus. ...
    (sci.math)
  • Re: surface area of n-dimensional sphere
    ... of n dimensions and wonder how to approach the problem. ... I'm only looking for hints, ... Note that a cross-section of an n dimensional sphere is an n-1 ... with calculus. ...
    (sci.math)
  • Re: solid angle
    ... >>its projection on the cylinder is itself a calculus (integration) ... >sphere with its polar caps lopped off, you can use Pappus' theorem ... I will stick by my statement that "to show an area on a sphere = the ...
    (sci.math)
  • Re: solid angle
    ... >>its projection on the cylinder is itself a calculus (integration) ... >sphere with its polar caps lopped off, you can use Pappus' theorem ... I will stick by my statement that "to show an area on a sphere = the ...
    (sci.physics)
  • Re: surface area of n-dimensional sphere
    ... sphere is 4pi, I'm curious about the general case ... of n dimensions and wonder how to approach the problem. ... I'm only looking for hints, ... Michael Press ...
    (sci.math)