How to solve a complicated equation?
조회 수: 3 (최근 30일)
이전 댓글 표시
There is a Equation G. How to obtain the values of α and β when G=0?
G=-(-Omega^3*tau + (alpha + beta)*Omega)^2 - (Omega^2 - alpha*f)^2.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/677023/image.png)
The answer:
alpha = Omega^2*cos(Omega*tau)/f;
beta = Omega*(f*sin(Omega*tau) - Omega*cos(Omega*tau))/f.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/677028/image.png)
CAN anyone help me with this issue??? Thanks!!!
댓글 수: 4
채택된 답변
David Goodmanson
2021년 7월 16일
편집: David Goodmanson
2021년 7월 16일
Hi Cola,
Since there is one equation and two unknowns, it must be possible to define, say, beta in terms of alpha, where alpha can be anything. For G = 0 we have
(-Om^3*t + (a+b)*Om)^2 = -(Om^2 - a*f)^2
so
-Om^3*t + (a+b)*Om = +-*i*(Om^2 - a*f)
where there are obvious notational substitutions for Omega, tau, alpha, beta, and the +- choice gives two different solutions. Solving for b,
b = (1/Om)*( Om^3*t -a*Om +-i*(Om^2 - a*f) )
where 'a' can be anything. Solving instead for a (this does not give a different family of solutions, rather the same ones expressed differently) gives
a = (Om^3*t +-i*Om^2 -b*Om)/(Om +-i*f)
Here the sign in the denominator (+ or -) has to match the sign in the denominator, and b can be anything. The choice b = 0 gives the solutions from Star Strider.
추가 답변 (0개)
참고 항목
카테고리
Help Center 및 File Exchange에서 Calculus에 대해 자세히 알아보기
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!