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Math Help - [SOLVED] Equation system to solve

  1. #1
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    [SOLVED] Equation system to solve

    Hi,

    Got this equation system to solve, and its just not going anywhere to me, keep banging a dead end... Hope you guys can help. The unknowns are d1 and d2, the rest is assumed as known.



    Any help appreciated!

    THNX!
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  2. #2
    Super Member Anonymous1's Avatar
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    Quote Originally Posted by crapmathematician View Post
    Hi,

    Got this equation system to solve, and its just not going anywhere to me, keep banging a dead end... Hope you guys can help. The unknowns are d1 and d2, the rest is assumed as known.



    Any help appreciated!

    THNX!
    x_1 - d_1 \sin x_1= x_2 + d_2 \cos x_2 \rightarrow(1)

    y_1 - d_1 \cos x_1= y_2 + d_2 \sin x_2 \rightarrow(2)

    Rearrange (1): x_1 - x_2 - d_2 \cos x_2 = d_1 \sin x_1

    \Rightarrow d_1 = \frac{x_1 - x_2 - d_2 \cos x_2}{\sin x_1} \rightarrow(3)

    Now sub (3) into (2) and solve for d_2.

    Then, plug the d_2 you found into (1) to find d_1.
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  3. #3
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    Quote Originally Posted by Anonymous1 View Post
    x_1 - d_1 \sin x_1= x_2 + d_2 \cos x_2 \rightarrow(1)

    y_1 - d_1 \cos x_1= y_2 + d_2 \sin x_2 \rightarrow(2)

    Rearrange (1): x_1 - x_2 - d_2 \cos x_2 = d_1 \sin x_1

    \Rightarrow d_1 = \frac{x_1 - x_2 - d_2 \cos x_2}{\sin x_1} \rightarrow(3)

    Now sub (3) into (2) and solve for d_2.

    Then, plug the d_2 you found into (1) to find d_1.

    That's where the problem is! When I put (3) into (2) to solve for d_1 I get a beast which looks like this:



    and I have no clue how to make it tidy to solve for d_1
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  4. #4
    Super Member Anonymous1's Avatar
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    \frac{x_1 \cos x_1 - x_2 \cos x_1 - d_2 \cos x_1 \cos x_2}{\sin x_1} = y_2 - y_1 + d_2 \sin x_2

    \implies x_1 \cos x_1 - x_2 \cos x_1 - d_2 \cos x_1 \cos x_2 = y_2 \sin x_1 - y_1 \sin x_1 + d_2 \sin x_2 \sin x_1

    \implies x_1 \cos x_1 - x_2 \cos x_1 - y_2 \sin x_1  + y_1 \sin x_1 = d_2 \sin x_2 \sin x_1 +  d_2 \cos x_1 \cos x_2

    \implies x_1 \cos x_1 - x_2 \cos x_1 - y_2\sin x_1 + y_1 \sin x_1 = d_2 (\sin x_2 \sin x_1 +  \cos x_1 \cos x_2 )

    \implies d_2 = \frac{x_1 \cos x_1 - x_2 \cos x_1 - y_2 \sin x_1 + y_1 \sin x_1}{\sin x_2 \sin x_1 +  \cos x_1 \cos x_2}.

    Yeah it's ugly, but I'm not sure I see the issue...?
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  5. #5
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    Change of situation!!!

    If I assume that I know d1 and d2 but do not know alpha1 and alpha2 instead. From equation 1 I have expressed sina1 which results as (x1-x2-d2*cosa2)/d1. How do I change this in order to be able to substitute for cosa1 in equation 2? Or is there another way to solve it?
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