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Solution for two unknowns with two equations

  1. Nov 24, 2014 #1
    lb*cos(qb) - lc*cos(qc) = ld*cos(qd) - la*cos(qa)

    lb*sin(qb) - lc*sin(qc) = ld*sin(qd) - la*sin(qa)


    Those are the equations I have. I know all the parameters but qb and qc.

    How can I solve for qb and qc ?
     
  2. jcsd
  3. Nov 24, 2014 #2
    This would mean the system is:

    B⋅cos x - C⋅cos y = D
    B⋅sin x - C⋅sin y = E

    ?
     
  4. Nov 24, 2014 #3

    mfb

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    Staff: Mentor

    There is always the approach ##\sin(x) = \sqrt{1-\cos^2(x)}##, but there might be a better solution for this particular set of equations.
     
  5. Nov 24, 2014 #4
    Yes
     
  6. Nov 24, 2014 #5
    Transform it into system of algebraic equation with tangent half-angle substitution:
    tan(x/2)=u ⇒ sin(x)=2u/(1+u2) , cos(x)=(1-u2)/(1+u2)
    tan(y/2)=v ⇒ sin(y)=2v/(1+v2) , cos(y)=(1-v2)/(1+v2).

    Unfortunatelly, it seems in general case the system can't be solved exactly,and you'll have to do it with aproximative numerical methods (iterativelly).

    *Post edited for removing typos
     
    Last edited: Nov 24, 2014
  7. Nov 24, 2014 #6

    mfb

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    Staff: Mentor

    It is possible to find an analytic solution. The common prefactors on the left side make it much easier.
     
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