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k
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s
{\displaystyle \left(a-x\right)k\,ds}
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s
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{\displaystyle \int {\frac {a-x}{r^{3}}}\,k\,s\,ds=-\int \left(a-x\right)k\,{\frac {\partial \left({\frac {1}{r}}\right)}{\partial s}}\,ds-\int {\frac {\left(a-x\right)^{2}}{r^{3}}}\,k\,{\frac {\partial a}{\partial s}}\,ds.}
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{
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k
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s
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d
s
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{\displaystyle {\begin{aligned}-\int \left(a-x\right)k{\frac {\partial \left({\frac {1}{r}}\right)}{\partial s}}ds=&-{\frac {\left(a-x\right)k}{r}}\\&+\int {\frac {1}{r}}\left\lbrace \left(a-x\right){\frac {\partial k}{\partial s}}+k{\frac {\partial a}{\partial s}}\right\rbrace ds.\\\end{aligned}}}
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{\displaystyle {\begin{aligned}\int {\frac {a-x}{r^{3}}}k\,s\,ds=&-{\frac {\left(a-x\right)k}{r}}+\int {\frac {a-x}{r}}{\frac {\partial k}{\partial s}}ds\\&+\int k{\frac {\partial a}{\partial s}}{\frac {r^{2}-\left(a-x\right)^{2}}{r^{3}}}ds,\\\end{aligned}}}
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r
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{\displaystyle {\begin{aligned}\int {\frac {a-x}{r^{3}}}k\,s\,ds=&-{\frac {\left(a-x\right)k}{r}}+\int {\frac {a-x}{r}}{\frac {\partial k}{\partial s}}ds\\&+\int k{\frac {s^{2}}{r^{3}}}{\frac {\partial a}{\partial s}}ds.\\\end{aligned}}}
0
{\displaystyle 0\,}
S
{\displaystyle S\,}
−
(
a
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x
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k
r
{\displaystyle -{\frac {\left(a-x\right)k}{r}}}
s
=
0
{\displaystyle s=0\,}
cos
α
=
1
{\displaystyle \cos \alpha =1\,}
k
=
ρ
0
.
{\displaystyle k=\rho _{0}\,.}
s
=
0
{\displaystyle s=0\,}
a
=
0
{\displaystyle a=0\,}
[
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r
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0
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2
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f
u
¨
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>
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¨
r
x
<
0.
{\displaystyle \left[-{\frac {a-x}{r}}\right]_{0}=-{\frac {-x}{\sqrt {\left(-x\right)^{2}}}}={\begin{cases}+1,&{\rm {{f{\ddot {u}}r}\;x>0,}}\\-1,&{\rm {{f{\ddot {u}}r}\;x<0.}}\end{cases}}}
Nehmen wir
x
=
0
{\displaystyle x=0\,}
a
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x
r
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2
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s
2
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a
s
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{\displaystyle {\frac {a-x}{r}}={\frac {a}{\sqrt {a^{2}+s^{2}}}}={\frac {\frac {a}{s}}{\sqrt {1+{\frac {a^{2}}{s^{2}}}}}}.}
a
s
{\displaystyle {\frac {a}{s}}}
s
=
0
{\displaystyle s=0\,}
x
{\displaystyle x\,}
![{\displaystyle \left[-{\frac {a-x}{r}}\right]_{0}=-{\frac {-x}{\sqrt {\left(-x\right)^{2}}}}={\begin{cases}+1,&{\rm {{f{\ddot {u}}r}\;x>0,}}\\-1,&{\rm {{f{\ddot {u}}r}\;x<0.}}\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1334cfcf87002d6c188c9a6544167f39b4659e81)
