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How can i simplify my equation

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esat gulhan
esat gulhan on 13 Sep 2020
Commented: Walter Roberson on 14 Sep 2020
Is ther anyway to simplify equation uo=-C/r , i want to explain uo with r not x and y
syms u uo ur v Q C x y r
u=C*y/(x^2+y^2)
v=-C*x/(x^2+y^2)
r=(x^2+y^2)^0.5
Q=atan(y/x)
ur=u*cos(Q)+v*sin(Q)
uo=-u*sin(Q)+v*cos(Q)
simplify(uo)

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Answers (1)

Walter Roberson
Walter Roberson on 13 Sep 2020
No, there isn't a way to simplify uo = -C/r, because it is not true.
If you substitute x = -7, y = 3 you will find that uo = C/r rather than -C/r
If you substitute x = 7, y = 3, you will find that uo = -C/r
The actual formula is that uo = -C * sign(x) / r

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esat gulhan
esat gulhan on 14 Sep 2020
It is true becase
r^2=x^2+y^2
uo=-C/(x*(y^2/x^2 + 1)^(1/2))
uo=-C/(x*((x^2+y^2)/x^2)^(1/2))
uo=-C/(x*((r^2)/x^2)^(1/2))
uo=-C/(x*((r/x))
uo=-C/(r)
when i substitute x = -7, y = 3 I find -0.131*C not -C/r
Walter Roberson
Walter Roberson on 14 Sep 2020
uo=-C/(x*((r^2)/x^2)^(1/2))
uo=-C/(x*((r/x))
The second of those two steps is fault. When x is negative, sqrt(x^2) is not x, it is -x . sqrt(x^2) is abs(x) for real-valued x. And abs(x)/x is not 1: it is sign(x)

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