How to find the maximum of symbolic equation which contains trigonometric terms?

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Akshay Pratap Singh 2022-8-29

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https://ww2.mathworks.cn/matlabcentral/answers/1789455-how-to-find-the-maximum-of-symbolic-equation-which-contains-trigonometric-terms

评论： Akshay Pratap Singh 2022-9-7

采纳的回答： Torsten

I am trying to find the maximum value of "P" in the following equation with respect to "theta". ""dP/dtheta = 0""

P = 0.5*gama*((H)^2)*(1-kv)*Kgama + q*H*(1-kv)*Kq

where

Kgama=((1+tan(beta)*tan(g))*tan(beta)+((1+tan(beta)*tan(g))^2/(tan(theta)-tan(g))))*((sin(theta-phi)+tan(psi)*cos(theta-phi))/(cos(beta+delta-theta+phi)));

Kq = (b/H)*cos(g)*((sin(theta-phi)+tan(psi)*cos(theta-phi))/(cos(beta+delta-theta+phi)));

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Torsten 2022-8-29

My first step would be to give values to the other parameters and plot P as a function of theta.

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Answer 1

Torsten 2022-8-29

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https://ww2.mathworks.cn/matlabcentral/answers/1789455-how-to-find-the-maximum-of-symbolic-equation-which-contains-trigonometric-terms#answer_1036740

编辑：Torsten 2022-8-29

在 MATLAB Online 中打开

syms gama H kv q beta phi g theta psi delta b

P = 0.5*gama*((H)^2)*(1-kv)*((1+tan(beta)*tan(g))*tan(beta)+((1+tan(beta)*tan(g))^2/(tan(theta)-tan(g))))*((sin(theta-phi)+tan(psi)*cos(theta-phi))/(cos(beta+delta-theta+phi)))+ q*H*(1-kv)*(b/H)*cos(g)*((sin(theta-phi)+tan(psi)*cos(theta-phi))/(cos(beta+delta-theta+phi)));

dPdtheta = diff(P,theta);

sol = simplify(solve(dPdtheta==0,theta))

sol =