Solving for unisolated variable

조회 수: 5(최근 30일)
Jonathan
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

답변(2개)

Walter Roberson
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)
  댓글 수: 2
Walter Roberson
Walter Roberson 2013년 11월 23일
I used a symbolic engine.

댓글을 달려면 로그인하십시오.


Roger Stafford
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.
  댓글 수: 3
Jonathan
Jonathan 2013년 11월 23일
Interesting... Thank you very much. I'll let you know if it accomplishes the task!

댓글을 달려면 로그인하십시오.

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by