User:!jim/Sandbox

$A_{0}=\alpha -{\frac {1}{\pi }}\int _{0}^{\pi }{\frac {d{\overline {Z}}}{dx}}(\theta )d\theta$

$A_{n}={\frac {2}{\pi }}\int _{0}^{\pi }{\frac {d{\overline {Z}}}{dx}}(\theta )\cos(n\theta )d\theta$

Load at point x

$L(x)=\int _{0}^{x}w(x^{*})dx^{*}=\int _{0}^{x}c{\sqrt {1-{\frac {4x^{*2}}{b^{2}}}}}dx^{*}$

where:

• $L(x)$ is the total force at point x
• $c={\frac {2\,\mathrm {weight} \,n_{max}}{a\pi }}$
• $b$ is the span
• $x^{*}$ is the integration variable (kinda like how sometimes you integrate in $\tau$ from 0 to t)

$\mathrm {centroid} ={\frac {\int _{0}^{x}x^{*}c{\sqrt {1-{\frac {4x^{*2}}{b^{2}}}}}dx^{*}}{\int _{0}^{x}c{\sqrt {1-{\frac {4x^{*2}}{b^{2}}}}}dx^{*}}}$