help with symbolic int result

Question

CD 2024-2-6

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2078541-help-with-symbolic-int-result

编辑： Walter Roberson 2024-2-6

采纳的回答： Walter Roberson

在 MATLAB Online 中打开

I ran into a problem, symbolic int results include int, adding a second variable, theta + psi, when using symbolic int.

Attached the "Code" and "Result" below.

Rather than randomly implementing all permutations of "assume()" and "simplify()" would someone please guide me to generating a result with the symsbolic "int" term?

Thank you

Code:

syms theta psi No Lo
N1          = (sym(1)/sym(2))*(No/sym(1))*sign(sin(sym(1)*theta + psi));
assume(theta>0 & theta<2*pi)
assume(theta, "real")
L11         = Lo*int((subs(N1,theta, theta + psi))^2, theta, 0, 2*pi)    
simplify(L11, Steps=10)

Result:

(Lo*No^2*int(sign(sin(theta + 2*psi))^2, theta, 0, 2*pi))/4

4 个评论
显示 2更早的评论隐藏 2更早的评论

CD 2024-2-6

编辑：Walter Roberson 2024-2-6

在 MATLAB Online 中打开

Difficult to explain.

If you look at the attached code, L11 is derived from N1, integrated over theta, and L22 is derived from N2, integrated over theta.

L12 is a derived from L11 and L22, intergrated over theta.

At the end, Matlab returns a single value (L12 = 68).

I would like to add a phase offset, psi, which exists in the final equation of L12.

This way I can find L12 (single value) given say L11 (or L22) is offset from L22 by a desired offset, psi.

No idea what to call this.

Hope this helps.

Thank you,

Example that returns a single value (after a bunch of steps):

syms theta No Lo
N1          = (sym(1)/sym(2))*(No/sym(1))*sign(sin(sym(1)*theta));
L11         = Lo*int(N1^2, theta, 0, 2*pi)
N2          = piecewise((0  < theta) & (theta < pi),   -(1/pi)*theta+0.5, ...
                        (pi < theta) & (theta < 2*pi),  (1/pi)*theta-1.5);
L22         = Lo*int(N2^2,theta,0,2*pi)
L12         = Lo*int(L11*L22,0, 2*pi) 
Lo = 1;
L12         = vpa(subs(L12), 4)

% L12 = 68.0 [units]

Torsten 2024-2-6

And what is your question ?

CD 2024-2-6

Torsten,

Walter Roberson is working this in a direction that I like.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Walter Roberson 2024-2-6

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2078541-help-with-symbolic-int-result#answer_1403251

编辑：Walter Roberson 2024-2-6

在 MATLAB Online 中打开

syms theta psi No Lo real

assumeAlso(theta>0 & theta<2*pi)

N1 = (sym(1)/sym(2))*(No/sym(1))*sign(sin(sym(1)*theta + psi));

L11 = Lo*int((subs(N1,theta, theta + psi))^2, theta, 0, 2*pi)

L11 =

simplify(L11, Steps=10)

ans =

The sign of psi is not defined, so this is the best you can do.

5 个评论
显示 3更早的评论隐藏 3更早的评论

CD 2024-2-6

编辑：Walter Roberson 2024-2-6

在 MATLAB Online 中打开

Ok, the output appears to be piecewise (view of live editor, not as obvious with script).

So I have seen this via script so at the time I did not know what to make of it.

I understand that this results essentually defines L11 for what may be all values of psi (assuming with 0 to 2pi).

How would I continue on with this L11 result?

How may I set or fix psi with in L11 then continue???

For example (there is a question in the middle of the example):

clc

clear all

syms theta psi No Lo real

assumeAlso(psi>0 & psi<2*pi)

N1 = (sym(1)/sym(2))*(No/sym(1))*sign(sin(sym(1)*theta + psi));

L11 = Lo*int((subs(N1,theta, theta + psi))^2, theta, 0, 2*pi)

L11 =

At this point L11 could be / is a function (piecewise) of psi.

How might I set psi (within L11) to some value/offset here then continue on with the following code???

%simplify(L11, Steps=10)

N2 = piecewise((0 < theta) & (theta < pi), -(1/pi)*theta+0.5, ...

(pi < theta) & (theta < 2*pi), (1/pi)*theta-1.5);

L22 = Lo*int(N2^2,theta,0,2*pi)

L22 =

L12 = Lo*int(L11*L22,0, 2*pi)

L12 =

Lo = 1, No = 1;

Lo = 1

L12 = vpa(subs(L12), 4) % L2 = xx [units]

L12 =

5.168

CD 2024-2-6

Perhaps better question:

Given my latest code list ...

Should I stop at the ouput of L11 then rebuild the derivation of L11 with psi removed given the piecewise results with psi then continue to derive L12?

Or is there a smarter way of getting to L12 with psi part of L11?