Solve a nonlinear equation
2 次查看(过去 30 天)
显示 更早的评论
Hi, Could you please help me to solve this equation in terms of "q"
1.082 [ (q-1) log((3/4 -3q/4)/(1-3q/4))+ q*log((3q/4) *(3/4 -3q/4)] + 1.4427[-3log(1-q/2) *((q/2) -1)+(q/2+1/2)^2 *log(q/2+1/2)- (3q/4 -1)*log(1-3q/4)- (3q/4+1/4)*log(3q/4+1/4)] + 0.7213[q*log(q/2)* ( -q-3/2 +1/q)+ (-q-1)*log(q/2 +1/2) + q*(-q/2+1/2)*log(1/2-q/2)-3*log(1-q/2)-(q-1)*log(1/2 - q/2)] -0.36 *[(q-1)^2*log(1/2 - q/2)]=0
2 个评论
采纳的回答
Walter Roberson
2013-11-18
If you assume natural logs, then there are no non-complex solutions.
The value of the expression (assuming natural logs) is negative between 0 and 1 (going to negative infinity at those two bounds.) Outside of that range, the expression is real-valued at exactly one point near -3.000138648 and at exactly one point near 1.851008154. At those two exceptional locations, the expression has positive non-zero values. The fact that there are negative values and positive values does not, however, imply that there are points at which the function is real-valued and 0, as the function is discontinuous.
The results have the same shape if log10 is used instead of ln.
6 个评论
Matt J
2013-11-18
Thanks, but the point is that we have another constraint that q only should get the values between 0 and 1 since its the value of probability density!
If you really mean "probability density" then q should be required to be positive, but not less than 1. Only probability mass functions and CDFs have that requirement.
更多回答(3 个)
Andrei Bobrov
2013-11-18
syms q
>> ex = 1.082*( (q-1)*log((3/4 -3*q/4)/(1-3*q/4))+ q*log((3*q/4) *(3/4 -3*q/4)) + 1.4427*(-3*log(1-q/2) *((q/2) -1)+(q/2+1/2)^2 *log(q/2+1/2)- (3*q/4 -1)*log(1-3*q/4)- (3*q/4+1/4)*log(3*q/4+1/4)) + 0.7213*(q*log(q/2)* ( -q-3/2 +1/q)+ (-q-1)*log(q/2 +1/2) + q*(-q/2+1/2)*log(1/2-q/2)-3*log(1-q/2)-(q-1)*log(1/2 - q/2)) -0.36 *((q-1)^2*log(1/2 - q/2)));
>>solve(ex,q)
ans =
- 3.7601288392107154402269169733539 + 0.46896675884329957486140629064384*i
0 个评论
cagatay yilmaz
2017-4-23
Hello,
Could you guys help me the solve following problem. This is the dispersion equation for a symmetric lamb wave. I am looking for the z values for different f (frequencies)? I have to find something similar to Fig 1 a.
close all
clear all
clc
%cl longitudunal wave speed
%ct transversal wave speed
%cp phase velocity of wave
%cg group velocity of wave
% z=ct/cp;
pi=3.14;
nu=0.33;% poisson ratio
ro=2700;%density kg/m3
E=70e9;% elastic modulus Pa
mu=E/(2*(1+nu)); %shear modulus
cl=((E*(1-nu))/(ro*(1+nu)*(1-2*nu)))^(0.5);
ct=(mu/ro).^(0.5);
k=ct/cl;
f=10:10:3e6;
w=2*pi*f;
d=(w*0.8e-3)/ct;
fzero (@(z) (2*z.^2-1).^2*(sin(sqrt((1-z.^2))*d))*cos(sqrt((k.^2-z.^2.*d)))-(sin(sqrt (k.^2-z.^2.*d)))*cos(sqrt((1-z.^2))*d)*(4*z.^2)*sqrt(1-z.^2)*sqrt(k.^2-z.^2),1)
2 个评论
cagatay yilmaz
2017-4-23
I have started a new question
https://www.mathworks.com/matlabcentral/answers/336873-nonlinear-tangent-trigonemetric-equation
另请参阅
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!