# Solving for unisolated variable

조회 수: 5(최근 30일)
Jonathan 2013년 11월 22일
댓글: Jonathan 2013년 11월 23일
Hello all, I'm having a bit of trouble finding a method to solve a nonlinear equation. I've looked into "fsolve" a little but couldn't figure out if it would be effective. I'm using MatLab 2009.
Here is the equation, for ease I've simplified the constants to A,B,C. Variable to solve for is x.
x = arctan( (A - C*cos(x)) / (B*cos(x)) )
Which was derived from
A = B*sin(x) + C*cos(x)
Any help would be greatly appreciated... Rather than relying on MatLab to solve I would like to have x = F(A,B,C) where A,B,C are known but change with each iteration.
Another consideration is that this value needs to be found 5-10 times per second.
Thank you in advance! - Jon

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### 답변(2개)

Walter Roberson 2013년 11월 22일
There are two solutions:
T0 = sqrt(C^2*B^2 - B^2*A^2 + B^4);
X = [(C*A + T0)/(C^2+B^2), (C*A - T0)/(C^2+B^2)]; %just sign difference between two
Y = (A - C*X) / B;
atan2(Y, X)
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Walter Roberson 2013년 11월 23일
I used a symbolic engine.

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Roger Stafford 2013년 11월 23일
Two solutions can be expressed as:
x = asin(A/sqrt(B^2+C^2)) - atan2(C,B);
and
x = pi - asin(A/sqrt(B^2+C^2)) - atan2(C,B)
Also either value with any integral multiple of 2*pi added or subtracted is a solution, thus giving infinitely many solutions.
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Jonathan 2013년 11월 23일
Interesting... Thank you very much. I'll let you know if it accomplishes the task!

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