How to find symbolic solution for theta1?

Question

safi58 2017-4-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/334533-how-to-find-symbolic-solution-for-theta1

评论： Manuela Gräfe 2017-4-24

clc
clear all
syms m_c_theta1 m_c0 M theta1 j_L0 j_L_theta1 l j_Lm_gama
syms m_c_theta2 theta2 j_L_theta2 m_c_gama k1 gama j_L_gama j_Lm0 j_Lm_theta1 j_Lm_theta2 fi
% k1=0.423;
% F=0.95;
% gama=pi/F;
% theta2=10,
% l=0.218;
% M=0.7;
eqn1=m_c_theta1==(m_c0-1/M-1)*cos(theta1)+j_L0*sin(theta1)+1/M+1;
eqn2=j_L_theta1==(-m_c0+1/M+1)*sin(theta1)+j_L0*cos(theta1);
%eqn3=m_m_theta1==1;
%eqn3=j_Lm_theta1==j_Lm0-l*theta1;

Hi all,

Can anyone help of finding a solution specially theta1 because I found others except theta1?

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Manuela Gräfe 2017-4-24

Hello umme mumtahina,

please send me an personal message. I am also interested in the solutions of your questions.

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Answer 1

Walter Roberson 2017-4-10

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https://ww2.mathworks.cn/matlabcentral/answers/334533-how-to-find-symbolic-solution-for-theta1#answer_262432

No.

If you solve the first 5 equations for m_c0, j_L0, m_c_theta1, j_L_theta2, m_c_theta2 and substitute that into the 6th equation, then the right hand side will equal the left hand side.

In other words you only have 5 independent equations, not 6.

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safi58 2017-4-10

编辑：Walter Roberson 2017-4-10

IS there any way to find a solution for theta1? after finding m_c0, j_L0, I have put it in eqn 2 where j_L_theta1=-(gama*l)/2; but it is giving me some weird answer like this:

-log((exp((theta2*1i)/2)*(exp(gama*2i) + 2*exp(gama*3i) + exp(gama*4i) + exp(theta2*2i) + M^2*exp(theta2*1i) + 2*exp(gama*1i)*exp(theta2*1i) + 2*exp(gama*1i)*exp(theta2*2i) + 4*exp(gama*2i)*exp(theta2*1i) + exp(gama*2i)*exp(theta2*2i) + 2*exp(gama*3i)*exp(theta2*1i) - 2*M^2*exp(gama*2i)*exp(theta2*1i) + M^2*exp(gama*4i)*exp(theta2*1i) - 4*M^2*j_L_theta1^2*exp(gama*2i)*exp(theta2*1i) + M^2*j_L_theta1*exp(gama*1i)*exp(theta2*1i)*4i - M^2*j_L_theta1*exp(gama*3i)*exp(theta2*1i)*4i - 8*M^2*j_L_theta1^2*exp(gama*2i)*exp(theta2*1i)*cos(gama) - 4*M^2*j_L_theta1^2*exp(gama*2i)*exp(theta2*1i)*cos(gama)^2 + M^2*j_L_theta1*exp(gama*1i)*exp(theta2*1i)*cos(gama)*4i - M^2*j_L_theta1*exp(gama*3i)*exp(theta2*1i)*cos(gama)*4i)^(1/2) + M*exp(theta2*1i) - M*exp(gama*2i)*exp(theta2*1i) + M*j_L_theta1*exp(gama*1i)*exp(theta2*1i)*2i + M*j_L_theta1*exp(gama*1i)*exp(theta2*1i)*cos(gama)*2i)/(exp(gama*1i) + exp(gama*2i) + exp(theta2*1i) + exp(gama*1i)*exp(theta2*1i)))*1i

-log((- exp((theta2*1i)/2)*(exp(gama*2i) + 2*exp(gama*3i) + exp(gama*4i) + exp(theta2*2i) + M^2*exp(theta2*1i) + 2*exp(gama*1i)*exp(theta2*1i) + 2*exp(gama*1i)*exp(theta2*2i) + 4*exp(gama*2i)*exp(theta2*1i) + exp(gama*2i)*exp(theta2*2i) + 2*exp(gama*3i)*exp(theta2*1i) - 2*M^2*exp(gama*2i)*exp(theta2*1i) + M^2*exp(gama*4i)*exp(theta2*1i) - 4*M^2*j_L_theta1^2*exp(gama*2i)*exp(theta2*1i) + M^2*j_L_theta1*exp(gama*1i)*exp(theta2*1i)*4i - M^2*j_L_theta1*exp(gama*3i)*exp(theta2*1i)*4i - 8*M^2*j_L_theta1^2*exp(gama*2i)*exp(theta2*1i)*cos(gama) - 4*M^2*j_L_theta1^2*exp(gama*2i)*exp(theta2*1i)*cos(gama)^2 + M^2*j_L_theta1*exp(gama*1i)*exp(theta2*1i)*cos(gama)*4i - M^2*j_L_theta1*exp(gama*3i)*exp(theta2*1i)*cos(gama)*4i)^(1/2) + M*exp(theta2*1i) - M*exp(gama*2i)*exp(theta2*1i) + M*j_L_theta1*exp(gama*1i)*exp(theta2*1i)*2i + M*j_L_theta1*exp(gama*1i)*exp(theta2*1i)*cos(gama)*2i)/(exp(gama*1i) + exp(gama*2i) + exp(theta2*1i) + exp(gama*1i)*exp(theta2*1i)))*1i

Walter Roberson 2017-4-10

If you comment out j_L_theta1=-(gama*I)/2 then the solution for theta1 appears to be

arctan((2^(1/2)*(-(cos(gama-theta2)-1)*(cos(theta2)-1)*((M^2*(j_L_theta1^2-1)*cos(theta2)-2*M^2*sin(theta2)*j_L_theta1-1)*cos(gama-theta2)-M^2*(2*j_L_theta1*cos(theta2)+sin(theta2)*(j_L_theta1^2-1))*sin(gama-theta2)-1+(j_L_theta1^2+1)*M^2))^(1/2)+M*((j_L_theta1*cos(theta2)+j_L_theta1-sin(theta2))*sin(gama-theta2)+(cos(gama-theta2)-1)*(sin(theta2)*j_L_theta1+cos(theta2)+1)))/sin(gama-theta2), (2^(1/2)*(cos(theta2)+1)*(-(cos(gama-theta2)-1)*(cos(theta2)-1)*((M^2*(j_L_theta1^2-1)*cos(theta2)-2*M^2*sin(theta2)*j_L_theta1-1)*cos(gama-theta2)-M^2*(2*j_L_theta1*cos(theta2)+sin(theta2)*(j_L_theta1^2-1))*sin(gama-theta2)-1+(j_L_theta1^2+1)*M^2))^(1/2)+M*((j_L_theta1*cos(theta2)+j_L_theta1-sin(theta2))*sin(gama-theta2)+(cos(gama-theta2)-1)*(sin(theta2)*j_L_theta1+cos(theta2)+1))*(cos(theta2)-1))/(sin(theta2)*sin(gama-theta2)))

or

arctan((-2^(1/2)*(-(cos(gama-theta2)-1)*(cos(theta2)-1)*((M^2*(j_L_theta1^2-1)*cos(theta2)-2*M^2*sin(theta2)*j_L_theta1-1)*cos(gama-theta2)-M^2*(2*j_L_theta1*cos(theta2)+sin(theta2)*(j_L_theta1^2-1))*sin(gama-theta2)-1+(j_L_theta1^2+1)*M^2))^(1/2)+M*((j_L_theta1*cos(theta2)+j_L_theta1-sin(theta2))*sin(gama-theta2)+(cos(gama-theta2)-1)*(sin(theta2)*j_L_theta1+cos(theta2)+1)))/sin(gama-theta2), (-2^(1/2)*(cos(theta2)+1)*(-(cos(gama-theta2)-1)*(cos(theta2)-1)*((M^2*(j_L_theta1^2-1)*cos(theta2)-2*M^2*sin(theta2)*j_L_theta1-1)*cos(gama-theta2)-M^2*(2*j_L_theta1*cos(theta2)+sin(theta2)*(j_L_theta1^2-1))*sin(gama-theta2)-1+(j_L_theta1^2+1)*M^2))^(1/2)+M*((j_L_theta1*cos(theta2)+j_L_theta1-sin(theta2))*sin(gama-theta2)+(cos(gama-theta2)-1)*(sin(theta2)*j_L_theta1+cos(theta2)+1))*(cos(theta2)-1))/(sin(theta2)*sin(gama-theta2)))

safi58 2017-4-18

Thanks Walter. I am working on it.

Manuela Gräfe 2017-4-24

Hello umme mumtahina,

please send me an personal message. I am also interested in the solutions of your questions.

Sometimes you just write: "Got it!", but you don't give the final solution. Due to the fact, that this is a public community, you should provide the corresponding answers to your questions.

So please send me ASAP a personal message.

请先登录，再进行评论。

How to find symbolic solution for theta1?

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