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Subject: Re: iterative convergence technique for kinematic solution
Date: Wed, 2 Jun 2010 18:27:20 +0000 (UTC)
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"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <hu567d$b5a$1@fred.mathworks.com>...
> ........
> This gives you 3 equations in 3 unknowns which you can use to solve for B(t). It is the intersection of 2 spheres and a plane.
- - - - - - - - - -
  You would do well to follow up on Matt's excellent advice.  You are starting with three equations in the cartesian coordinates of the unknown point.  One of them is linear and two are second degree equations.  By subtracting appropriately to eliminate the squared terms you can obtain a second linear equation from the two second degree equations.  The solution to the two linear equations is a line in which you can express each coordinate linearly in terms of a common parameter.  When you substitute these into one of the second degree equations, the result will be a quadratic equation with the single parameter as the unknown.  As is true of all quadratic equations, it will have either two roots, one double root, or no real roots.  As Matt has said, there is no need to use iteration to solve this elementary problem.

Roger Stafford