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MathGroup Archive 2001

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Re: Functions and Packages

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26981] Re: Functions and Packages
  • From: paradaxiom at my-deja.com
  • Date: Tue, 30 Jan 2001 03:38:29 -0500 (EST)
  • References: <94r6u9$id9@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

The problem was that f contained global versions of x and y,
whereas EulerEquations[...] was called with local versions
of x and y. Below is a complete solution to your problem,
I believe. Let me know if this is not the case:

BeginPackage["Extremal`", {"Calculus`VariationalMethods`"}]

Extremal::usage = "Usage: Extremal[ { f[ <<x, y[x]>> ], y[x], x } , {a,
b}, yy ] " ;

Begin["`Private`"]

Extremal[ { f_, y_[x_], x_ }, { a_, b_ } , yy:{__List} ] :=
Module[
        { w = Length[yy]-1, q, s }
        ,
        q = Table[ Derivative[n][y] /@ {a,b} , {n, 0, w} ] // Flatten ;
        q = Thread[ q == Flatten[yy] ] ;
        s = EulerEquations[ f, y[x], x ] ;
        s = Prepend[ q, s ];
        DSolve[ s, y[x], x ]
        ]

End[]

EndPackage[]



math
Mathematica 4.1 for Linux
Copyright 1988-2000 Wolfram Research, Inc.
 -- Motif graphics initialized --

In[1]:= <<Extremal`

In[2]:= ?Extremal
Usage: Extremal[ { f[ <<x, y[x]>> ], y[x], x } , {a, b}, yy ]

In[3]:= Extremal[ {360 x^2 y[x]-y''[x]^2,y[x],x},{0,1},{{0,0},{0,5/2}}]

                      2    3    6
                  -2 x  + x  + x
Out[3]= {{y[x] -> ---------------}}
                         2



//Marten


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