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Thread: Minimise the Maximum Value

  1. #1
    Oct 2007

    Minimise the Maximum Value

    I have two simple vector equations:
    \vec{L_{T}}=\sum_{i=0}^n{\vec{F_{i}} \times \vec{H_{i}}} : ( \times being the vector (aka cross) product).
    I know \vec{F_{T}} , \vec{L_{T}} and all values of \vec{H_{i}}. I want to find sensible values for the \vec{F_{i}} .

    When n = 2 this is a simple simultaneous equation.
    However when n > 2 there is no single point solution.
    Consider n=3; one could view the two equations as defining planes, the intersection of these planes would then define a line of points that satisfy the two equations.
    What I want is the solution from this range that minimises the largest value of \vec{F_{i}}.

    My current thinking is set all except 2 of the \vec{F_{i}} to zero and solve the resulting simultaneous equation.
    Repeat for a different pair of \vec{F_{i}}
    This gives two points on the solution line.
    Find the perpendicular to this line that passes through the origin (All \vec{F_{i}}=0)

    Am I looking in the correct area? Can someone point the way forward please.
    Last edited by Mark@Work; Oct 24th 2007 at 09:04 AM. Reason: Improved LaTex skills
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