set first derivative equal to zero with some constant

Question

nirwana 2023-5-14

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1962729-set-first-derivative-equal-to-zero-with-some-constant

编辑： Torsten 2023-5-14

I have equation from derive from snellius law and i'd like to set its derivative equal to zero since fermat principle said so.

here the matlab that I used to get fist derivative, but when I solve it in order to get x value when dT/dt=0 it give me strange result. Is it because I put a lot of variable in syms? actually a, b, c, v1 and v2 is a constant. should I put it a number rather than a alphabet symbol to get proper result?

syms x a b c v1 v2

T=sqrt(x.^2+a^2)./v1+sqrt((b-x).^2+c^2)./v2;

dTdx=diff(T)

dTdx =

fermat=solve(dTdx==0,x)

fermat =

2 个评论
显示无隐藏无

Matt J 2023-5-14

编辑：Matt J 2023-5-14

but when I solve it in order to get x value when dT/dt=0 it give me strange result.

What's the result, and what is strange about it?

Dyuman Joshi 2023-5-14

What are you solving with dTdx == 0 is a polynomial in x, and thus you are getting the roots of the polynomial as the output, in terms of the variables.

"actually a, b, c, v1 and v2 is a constant. should I put it a number rather than a alphabet symbol to get proper result?"

Yes. If you want Numerical solution, you will have to define the variables with numerical values.

Use double() if you want to convert the symbolic result into numerical result

请先登录，再进行评论。

请先登录，再回答此问题。