FANDOM


\frac{1}{p-m} = \sum_{n=1}^{\infty} (m^{n-1}*p^{-n})


t + c_1 = \frac{2\sqrt{x}\sqrt{a-bx}\arctan{\sqrt{\frac{bx}{a-bx}}}}{\sqrt{bx(a-bx)}}

\frac{2r_Wr_L\theta_i}{r_A} - \frac{2r_Wr_L^2\mu_{AC}m_Cg}{\kappa r_A}

\frac{2r_Wr_L}{r_A} \Big ( \theta_i - \frac{r_L\mu_{AC}m_Cg}{\kappa} \Big )


Project Edit

Overall Edit

r(\theta(j), f(h(j))) = \sqrt { (x_s(h(j))-x_r(j))^2 + (y_s(h(j))-y_r(j))^2 + (z_s(h(j))-z_r(j))^2 }


r(\theta(j), f(h(j))) = \sqrt { (x_s(((x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang)) \cos (elevang) + (z_r(j)-z_s) \sin (elevang))-x_r(j))^2 + (y_s(((x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang)) \cos (elevang) + (z_r(j)-z_s) \sin (elevang))-y_r(j))^2 + (z_s(((x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang)) \cos (elevang) + (z_r(j)-z_s) \sin (elevang))-z_r(j))^2 }

Part 1 Edit

r(\theta(j), f(h(j))) = \sqrt { \underbrace{(x_s(h(j))-x_r(j))^2} + (y_s(h(j))-y_r(j))^2 + (z_s(h(j))-z_r(j))^2 }


(x_s(((x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang)) \cos (elevang) + (z_r(j)-z_s) \sin (elevang))-x_r(j))^2


((((x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang)) \cos (elevang) + (z_r(j)-z_s) \sin (elevang))\cos(xyang)\cos(elevang)+x_s-x_r(j))^2


((((x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang)) \cos (xyang) (\cos (elevang))^2 + (z_r(j)-z_s) \cos (xyang) \cos (elevang) \sin (elevang))+x_s-x_r(j))^2


\langle \lbrace [(x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang)] \cos (xyang) (\cos (elevang))^2 + (z_r(j)-z_s) \cos (xyang) \cos (elevang) \sin (elevang) \rbrace +x_s-x_r(j) \rangle ^2


\Bigg( \bigg( \Big((x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang)\Big) \cos (xyang) \cos^2 (elevang) + (z_r(j)-z_s) \cos (xyang) \cos (elevang) \sin (elevang) \bigg) +x_s-x_r(j) \Bigg) ^2


\Bigg( \bigg( \Big((j\cos(rayxy)\cos(rayelev)+x_r-x_s) \cos (xyang) + (j\sin(rayxy)\cos(rayelev)+y_r-y_s) \sin (xyang)\Big) \cos (xyang) \cos^2 (elevang) + (j\sin(rayelev)+z_r-z_s) \cos (xyang) \cos (elevang) \sin (elevang) \bigg) +x_s-j\cos(rayxy)\cos(rayelev)-x_r \Bigg) ^2


\Bigg( \bigg( \underbrace{\Big((j\cos(rayxy)\cos(rayelev)+x_r-x_s) \cos (xyang) + (j\sin(rayxy)\cos(rayelev)+y_r-y_s) \sin (xyang)\Big)} \cos (xyang) \cos^2 (elevang) + (j\sin(rayelev)+z_r-z_s) \cos (xyang) \cos (elevang) \sin (elevang) \bigg) +x_s-j\cos(rayxy)\cos(rayelev)-x_r \Bigg) ^2


j\cos(xyang)\cos(rayxy)\cos(rayelev)+(x_r-x_s)\cos(xyang) + j\sin(xyang)\sin(rayxy)\cos(rayelev)+(y_r-y_s)\sin(xyang)


j(\cos(xyang)\cos(rayxy)\cos(rayelev) + \sin(xyang)\sin(rayxy)\cos(rayelev)) + (x_r-x_s)\cos(xyang) + (y_r-y_s)\sin(xyang)


\Bigg( \bigg( \Big(j(\cos(xyang)\cos(rayxy)\cos(rayelev) + \sin(xyang)\sin(rayxy)\cos(rayelev)) + (x_r-x_s)\cos(xyang) + (y_r-y_s)\sin(xyang)\Big) \cos (xyang) \cos^2 (elevang) + (j\sin(rayelev)+z_r-z_s) \cos (xyang) \cos (elevang) \sin (elevang) \bigg) +x_s-j\cos(rayxy)\cos(rayelev)-x_r \Bigg) ^2


\Bigg( \bigg( \underbrace{\Big(j(\cos(xyang)\cos(rayxy)\cos(rayelev) + \sin(xyang)\sin(rayxy)\cos(rayelev)) + (x_r-x_s)\cos(xyang) + (y_r-y_s)\sin(xyang)\Big) \cos (xyang) \cos^2 (elevang)} + (j\sin(rayelev)+z_r-z_s) \cos (xyang) \cos (elevang) \sin (elevang) \bigg) +x_s-j\cos(rayxy)\cos(rayelev)-x_r \Bigg) ^2


j\cos(xyang)\cos^2(elevang)\cos(rayelev)(\cos(xyang)\cos(rayxy) + \sin(xyang)\sin(rayxy)) + (x_r-x_s)\cos^2(xyang)\cos^2(elevang) + (y_r-y_s)\cos(xyang)\sin(xyang)\cos^2(elevang)


\Bigg( \bigg( j\cos(xyang)\cos^2(elevang)\cos(rayelev)(\cos(xyang)\cos(rayxy) + \sin(xyang)\sin(rayxy)) + (x_r-x_s)\cos^2(xyang)\cos^2(elevang) + (y_r-y_s)\cos(xyang)\sin(xyang)\cos^2(elevang) + (j\sin(rayelev)+z_r-z_s) \cos (xyang) \cos (elevang) \sin (elevang) \bigg) +x_s-j\cos(rayxy)\cos(rayelev)-x_r \Bigg) ^2


\Bigg( \bigg( j\cos(xyang)\cos^2(elevang)\cos(rayelev)(\cos(xyang)\cos(rayxy) + \sin(xyang)\sin(rayxy)) + (x_r-x_s)\cos^2(xyang)\cos^2(elevang) + (y_r-y_s)\cos(xyang)\sin(xyang)\cos^2(elevang) + \underbrace{(j\sin(rayelev)+z_r-z_s) \cos (xyang) \cos (elevang) \sin (elevang)} \bigg) +x_s-j\cos(rayxy)\cos(rayelev)-x_r \Bigg) ^2


(j\sin(rayelev)+z_r-z_s)\cos(xyang)\cos(elevang)\sin(elevang)
j\cos(xyang)\cos(elevang)\sin(elevang)\sin(rayelev)+(z_r-z_s)\cos(xyang)\cos(elevang)\sin(elevang)


\Bigg( \bigg( j\cos(xyang)\cos^2(elevang)\cos(rayelev)(\cos(xyang)\cos(rayxy) + \sin(xyang)\sin(rayxy)) + (x_r-x_s)\cos^2(xyang)\cos^2(elevang) + (y_r-y_s)\cos(xyang)\sin(xyang)\cos^2(elevang) + j\cos(xyang)\cos(elevang)\sin(elevang)\sin(rayelev)+(z_r-z_s)\cos(xyang)\cos(elevang)\sin(elevang) \bigg) +x_s-j\cos(rayxy)\cos(rayelev)-x_r \Bigg) ^2


\Bigg( \bigg( j(\cos^2(xyang)\cos^2(elevang)\cos(rayxy)\cos(rayelev) + \cos(xyang)\sin(xyang)\cos^2(elevang)\sin(rayxy)\cos(rayelev)) + (x_r-x_s)\cos^2(xyang)\cos^2(elevang) + (y_r-y_s)\cos(xyang)\sin(xyang)\cos^2(elevang) + j\cos(xyang)\cos(elevang)\sin(elevang)\sin(rayelev)+(z_r-z_s)\cos(xyang)\cos(elevang)\sin(elevang) \bigg) +x_s-j\cos(rayxy)\cos(rayelev)-x_r \Bigg) ^2


\Bigg( \bigg( j(\cos^2(xyang)\cos^2(elevang)\cos(rayxy)\cos(rayelev) + \cos(xyang)\sin(xyang)\cos^2(elevang)\sin(rayxy)\cos(rayelev) + \cos(xyang)\cos(elevang)\sin(elevang)\sin(rayelev)) + (x_r-x_s)\cos^2(xyang)\cos^2(elevang) + (y_r-y_s)\cos(xyang)\sin(xyang)\cos^2(elevang) + (z_r-z_s)\cos(xyang)\cos(elevang)\sin(elevang) \bigg) +x_s-j\cos(rayxy)\cos(rayelev)-x_r \Bigg) ^2


\Bigg(  j(\cos^2(xyang)\cos^2(elevang)\cos(rayxy)\cos(rayelev) + \cos(xyang)\sin(xyang)\cos^2(elevang)\sin(rayxy)\cos(rayelev) + \cos(xyang)\cos(elevang)\sin(elevang)\sin(rayelev) - \cos(rayxy)\cos(rayelev)) + (x_r-x_s)\cos^2(xyang)\cos^2(elevang) + (y_r-y_s)\cos(xyang)\sin(xyang)\cos^2(elevang) + (z_r-z_s)\cos(xyang)\cos(elevang)\sin(elevang) + x_s - x_r \Bigg) ^2


\Bigg(  j(\cos^2(xyang)\cos^2(elevang)\cos(rayxy)\cos(rayelev) + \cos(xyang)\sin(xyang)\cos^2(elevang)\sin(rayxy)\cos(rayelev) + \cos(xyang)\cos(elevang)\sin(elevang)\sin(rayelev) - \cos(rayxy)\cos(rayelev)) + (x_r-x_s)\cos^2(xyang)\cos^2(elevang) + (y_r-y_s)\cos(xyang)\sin(xyang)\cos^2(elevang) + (z_r-z_s)\cos(xyang)\cos(elevang)\sin(elevang) - (x_r-x_s) \Bigg) ^2


\Bigg( j(\cos^2(xyang)\cos^2(elevang)\cos(rayxy)\cos(rayelev) + \cos(xyang)\sin(xyang)\cos^2(elevang)\sin(rayxy)\cos(rayelev) + \cos(xyang)\cos(elevang)\sin(elevang)\sin(rayelev) - \cos(rayxy)\cos(rayelev)) + (x_r-x_s)(\cos^2(xyang)\cos^2(elevang)-1) + (y_r-y_s)\cos(xyang)\sin(xyang)\cos^2(elevang) + (z_r-z_s)\cos(xyang)\cos(elevang)\sin(elevang) \Bigg) ^2

h(j) Edit

h(j)=\sqrt { ((x_r(j)-x_s)^2 + y_r(j)-y_s)^2) * (\cos (\arctan (\frac{y_r(j)-y_s}{x_r(j)-x_s}) - xyang ) )^2 + (z_r(j)-z_s)^2 } * \cos (\arctan (\frac{z_r(j)-z_s}{ \sqrt{(x_r(j)-x_s)^2 + (y_r(j)-y_s)^2} * \cos (\arctan (\frac{y_r(j)-y_s}{x_r(j)-x_s}) - xyang) }) - elevang)


h(j)=\sqrt { ((x_r(j)-x_s)^2 + y_r(j)-y_s)^2) * (\frac{(x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang)}{\sqrt{(x_r(j)-x_s)^2 + (y_r(j)-y_s)^2}})^2 + (z_r(j)-z_s)^2 } * \cos (\arctan (\frac{z_r(j)-z_s}{ \sqrt{(x_r(j)-x_s)^2 + (y_r(j)-y_s)^2} * \frac{(x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang)}{\sqrt{(x_r(j)-x_s)^2 + (y_r(j)-y_s)^2}} }) - elevang)


h(j)=\sqrt { ((x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang))^2 + (z_r(j)-z_s)^2 } * \cos (\arctan (\frac{z_r(j)-z_s}{(x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang) }) - elevang)


h(j)=((x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang)) \cos (elevang) + (z_r(j)-z_s) \sin (elevang)


h(j)=(j\cos(xyang)\cos(rayxy)\cos(rayelev) + (x_r-x_s)\cos(xyang) + j\sin(xyang)\sin(rayxy)\cos(rayelev) + (y_r-y_s)\sin(xyang))\cos(elevang) + (j\sin(rayelev)+z_r-z_s)\sin(elevang)


h(j)=(j(\cos(xyang)\cos(rayxy)\cos(rayelev) + \sin(xyang)\sin(rayxy)\cos(rayelev)) + (x_r-x_s)\cos(xyang) + (y_r-y_s)\sin(xyang))\cos(elevang) + (j\sin(rayelev)+z_r-z_s)\sin(elevang)


h(j)=j(\cos(xyang)\cos(elevang)\cos(rayxy)\cos(rayelev) + \sin(xyang)\cos(elevang)\sin(rayxy)\cos(rayelev)) + (x_r-x_s)\cos(xyang)\cos(elevang) + (y_r-y_s)\sin(xyang)\cos(elevang) + (j\sin(rayelev)+z_r-z_s)\sin(elevang)


h(j)=j(\cos(xyang)\cos(elevang)\cos(rayxy)\cos(rayelev) + \sin(xyang)\cos(elevang)\sin(rayxy)\cos(rayelev)) + (x_r-x_s)\cos(xyang)\cos(elevang) + (y_r-y_s)\sin(xyang)\cos(elevang) + j\sin(elevang)\sin(rayelev) + (z_r-z_s)\sin(elevang)


h(j)=j(\cos(xyang)\cos(elevang)\cos(rayxy)\cos(rayelev) + \sin(xyang)\cos(elevang)\sin(rayxy)\cos(rayelev) + \sin(elevang)\sin(rayelev)) + (x_r-x_s)\cos(xyang)\cos(elevang) + (y_r-y_s)\sin(xyang)\cos(elevang) + (z_r-z_s)\sin(elevang)

Conversion Edit

\frac{(x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang)}{\sqrt{(x_r(j)-x_s)^2 + (y_r(j)-y_s)^2}} = \cos (\arctan (\frac{y_r(j)-y_s}{x_r(j)-x_s}) - xyang )

θ(j) Edit

\theta(j) = \arctan ( \frac{\sqrt{(x_r(j)-x_s)^2 + (y_r(j)-y_s)^2} * \sin (\arctan (\frac{y_r(j)-y_s}{x_r(j)-x_s})-xyang)}{\sqrt { ((x_r(j)-x_s)^2 + y_r(j)-y_s)^2) * (\cos (\arctan (\frac{y_r(j)-y_s}{x_r(j)-x_s}) - xyang ) )^2 + (z_r(j)-z_s)^2 } * \sin (\arctan (\frac{z_r(j)-z_s}{ \sqrt{(x_r(j)-x_s)^2 + (y_r(j)-y_s)^2} * \cos (\arctan (\frac{y_r(j)-y_s}{x_r(j)-x_s}) - xyang) }) - elevang)} ) - axisang


\theta(j) = \arctan ( \frac{(y_r(j)-y_s) \cos (xyang) - (x_r(j)-x_s) \sin (xyang)}{\sqrt { ((x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang))^2 + (z_r(j)-z_s)^2 } * \sin (\arctan (\frac{z_r(j)-z_s}{ (x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang) }) - elevang)} ) - axisang


\theta(j) = \arctan ( \frac{(y_r(j)-y_s) \cos (xyang) - (x_r(j)-x_s) \sin (xyang)}{(z_r(j)-z_s) \cos (elevang) - ((x_r(j)-x_s) \cos (xyang) + (y_r(j)-y_s) \sin (xyang)) \sin (elevang)} ) - axisang


\theta(j) = \arctan ( \frac{\cot (xyang) -  \tan (xyang)}{ \frac{z_r(j)-z_s}{(y_r(j)-y_s) \sin (xyang) + (x_r(j)-x_s) \cos (xyang)} \cos (elevang) - \sin (elevang)} ) - axisang

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