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FindRoot and vector equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg36254] FindRoot and vector equations
  • From: anhjunk at hotmail.com (anhjunk)
  • Date: Wed, 28 Aug 2002 04:16:15 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I need some help with using FindRoot. I want to solve a system of
nonlinear equations numerically. Each equation in the system is an
equation with vector variables. The equations are such that it is
difficult to convert them to equations involving only the components
of the vector variables.

I have tried the following two possibilities without success. In what
follows I am using a MADE UP EXAMPLE. In this example it is easy to
write the equations in terms of only the components. Furthermore the
correct solution is obvious. But I made up the example for
illustration only.

----------------------------Try
1--------------------------------------------

q = {{x[1], y[1]}, {x[2], y[2]}};
FindRoot[{q[[1]] + q[[2]] Sqrt[q[[2]].q[[2]]] == {0, 0}, 
    q[[1]] + q[[2]] == {0, 0}}, {q[[1]], {0, 0}}, {q[[2]], {0, 0}}]

This results in the error message :

FindRoot::"fddis": Start specification {q[[1]],{0,0}} does not contain
distinct
starting values.


----------------------------Try
2---------------------------------------------

FindRoot[{q[[1]] + q[[2]] Sqrt[q[[2]].q[[2]]] == {0, 0}, 
    q[[1]] + q[[2]] == {0, 0}}, {x[1], 0}, {x[2], 0}, {y[1], 0},
{y[2], 0}]

This results in the error message :

FindRoot::"frnum": "Function {0.,0.},{0.,0.}} is not a length 4 list
of numbers at {x[1],x[2],y[1],y[2]} = {0., 0., 0., 0.}

Questions 

1) How do I fix these two methods ? 
2) What do the error messages mean ?

Please keep in mind that this example is made up and trivial to solve
without Mathematica. It is being used for illustration purpose only.

Thanks


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