How to solve a complicated algebraic equation with symbolic toolbox?

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Giuseppe 2022-3-9

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https://ww2.mathworks.cn/matlabcentral/answers/1667259-how-to-solve-a-complicated-algebraic-equation-with-symbolic-toolbox

编辑： Torsten 2022-3-9

采纳的回答： Torsten

Hi guys,

In the following image there are some expression of some parameters.

I need to solve the equality deriving from expression (17), i.e.

in order to get

I tried to solve the problem by hand but it involves many substitutions and it is full of computations.

Is there a way to perform this task by using the symbolic toolbox with as little effort as possible?

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Torsten 2022-3-9

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1667259-how-to-solve-a-complicated-algebraic-equation-with-symbolic-toolbox#answer_913474

在 MATLAB Online 中打开

Either

delta_w = k*pi (k integer)

delta_w = acos(((p1*e2)^2 + (p2*e1)^2 - (p1-p2)^2)/(2*p1*p2*e1*e2))

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Giuseppe 2022-3-9

Yes, sorry. I meant the MATLAB code! Thank you.

Torsten 2022-3-9

编辑：Torsten 2022-3-9

在 MATLAB Online 中打开

Since I don't have MATLAB available at the moment:

Do you get the same formula from MATLAB as the one from my hand calculation or

         /      _____________________________________________________________\
         |     /  /  2   2                     2   2     2               2\  |
         |    /  -\e1 *p2  - 2*e1*e2*p1*p2 + e2 *p1  - p1  + 2*p1*p2 - p2 /  |
+/-2*atan|   /   ----------------------------------------------------------- |
         |  /        2   2                     2   2     2               2   |
         \\/       e1 *p2  + 2*e1*e2*p1*p2 + e2 *p1  - p1  + 2*p1*p2 - p2    /