Geometry:WAXS 3D - Revision history

KevinYager at 13:06, 10 August 2017

2017-08-10T13:06:42Z

2016-01-13T21:21:06Z

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2016-01-13T20:25:59Z

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2016-01-13T19:20:26Z

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2016-01-13T19:14:21Z

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2016-01-13T19:10:03Z

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2016-01-13T19:05:47Z

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2016-01-13T18:58:41Z

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2016-01-13T18:54:17Z

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2016-01-13T18:49:15Z

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@@ Line 242: / Line 242: @@
 \end{alignat}
 </math>
 =See Also=
 * [[Geometry:TSAXS 3D]]

@@ Line 182: / Line 182: @@
 \end{alignat}
 </math>
 =See Also=
 * [[Geometry:TSAXS 3D]]

@@ Line 182: / Line 182: @@
 \end{alignat}
 </math>
 =See Also=
 * [[Geometry:TSAXS 3D]]

← Older revision		Revision as of 19:20, 13 January 2016
Line 221:		Line 221:
	& = 2 d^{\prime 2} - 2 d^{\prime} x \sin \phi_g + ( x \sin \phi_g \cos \phi_g - 2 d^{\prime} \cos \phi_g )( d \cos \theta_g - z \sin \theta_g ) \\		& = 2 d^{\prime 2} - 2 d^{\prime} x \sin \phi_g + ( x \sin \phi_g \cos \phi_g - 2 d^{\prime} \cos \phi_g )( d \cos \theta_g - z \sin \theta_g ) \\

−	& = 2 d^{\prime 2} - 2 d^{\prime} x \sin \phi_g + ( x \sin ~~\phi_g \cos~~ \phi_g - 2 d^{\prime} \cos \phi_g )( d \cos \theta_g - z \sin \theta_g ) \\	+	& = 2 d^{\prime 2} - 2 d^{\prime} x \sin \phi_g + ( x \sin \phi_g - 2 d^{\prime} )\cos \phi_g( d \cos \theta_g - z \sin \theta_g ) \\

@@ Line 213: / Line 213: @@
        & + d^{\prime 2} \\
        & + d^2 \sin^2 \theta_g + 2 d z \sin \theta_g \cos \theta_g + z^2 \cos^2 \theta_g ] \end{alignat} \\
      & = ? \\

← Older revision		Revision as of 19:10, 13 January 2016
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	& + d^2 \sin^2 \theta_g + 2 d z \sin \theta_g \cos \theta_g + z^2 \cos^2 \theta_g ] \end{alignat} \\		& + d^2 \sin^2 \theta_g + 2 d z \sin \theta_g \cos \theta_g + z^2 \cos^2 \theta_g ] \end{alignat} \\

		+	& = \begin{alignat}{2} [
		+	& x^2 + d^2 \cos^2 \theta_g - 2 dz \cos \theta_g \sin \theta_g + z^2 \sin^2 \theta_g \\
		+	& + ( - x \sin \phi_g \cos \phi_g + 2 x \sin \phi_g \cos \phi_g - 2 d^{\prime} \cos \phi_g )( d \cos \theta_g - z \sin \theta_g ) \\
		+	& - 2 d^{\prime} x \sin \phi_g \\
		+	& + d^{\prime 2} \\
		+	& + d^2 \sin^2 \theta_g + 2 d z \sin \theta_g \cos \theta_g + z^2 \cos^2 \theta_g ] \end{alignat} \\

	& = ? \\		& = ? \\

@@ Line 200: / Line 200: @@
        & + \cos^2 \phi_g ( d \cos \theta_g - z \sin \theta_g )^2 - 2 d^{\prime} \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) + d^{\prime 2} \\
        & + d^2 \sin^2 \theta_g + 2 d \sin \theta_g z \cos \theta_g + z^2 \cos^2 \theta_g ] \end{alignat} \\
      & = ? \\

@@ Line 197: / Line 197: @@
      & = \begin{alignat}{2} [
        & x^2 \cos^2 \phi_g - x \cos \phi_g \sin \phi_g ( d \cos \theta_g - z \sin \theta_g ) + \sin^2 \phi_g ( d \cos \theta_g - z \sin \theta_g )^2  \\
-       & + x^2 \sin^2 \phi_g + 2 x \sin \phi_g \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) - d^{\prime} x \sin \phi_g \\
+       & + x^2 \sin^2 \phi_g + 2 x \sin \phi_g \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) - 2 d^{\prime} x \sin \phi_g \\
-       & + \cos^2 \phi_g ( d \cos \theta_g - z \sin \theta_g )^2 - d^{\prime} \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) \\
+       & + \cos^2 \phi_g ( d \cos \theta_g - z \sin \theta_g )^2 - 2 d^{\prime} \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) + d^{\prime 2} \\
        & + d^2 \sin^2 \theta_g + 2 d \sin \theta_g z \cos \theta_g + z^2 \cos^2 \theta_g ] \end{alignat} \\

@@ Line 192: / Line 192: @@
        & + x^2 \sin^2 \phi_g + x \sin \phi_g \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) - d^{\prime} x \sin \phi_g \\
        & + \cos \phi_g ( d \cos \theta_g - z \sin \theta_g )x \sin \phi_g + \cos^2 \phi_g ( d \cos \theta_g - z \sin \theta_g )^2 - d^{\prime} \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) \\
        & - d^{\prime} x \sin \phi_g - d^{\prime} \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) + d^{\prime 2} \\
        & + d^2 \sin^2 \theta_g + 2 d \sin \theta_g z \cos \theta_g + z^2 \cos^2 \theta_g ] \end{alignat} \\
@@ Line 197: / Line 204: @@
      & = ? \\
      & = ? \\
      & = 2 d^{\prime} \left( d^{\prime} - x \sin \phi_g + \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) \right) \\
 \left( \frac{q}{k} \right)^2

@@ Line 186: / Line 186: @@
 \begin{alignat}{2}
 \left ( \frac{q}{k} \right )^2 d^{\prime 2}
-     & = \begin{alignat}{2} & \left( x \cos \phi_g -\sin \phi_g ( d \cos \theta_g - z \sin \theta_g ) \right)^2 \\ & + \left( x \sin \phi_g + \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) - d^{\prime} \right)^2 \\ & + \left( d \sin \theta_g + z \cos \theta_g \right)^2 \end{alignat} \\
+     & = \begin{alignat}{2} [ & \left( x \cos \phi_g -\sin \phi_g ( d \cos \theta_g - z \sin \theta_g ) \right)^2 \\ & + \left( x \sin \phi_g + \cos \phi_g ( d \cos \theta_g - z \sin \theta_g ) - d^{\prime} \right)^2 \\ & + \left( d \sin \theta_g + z \cos \theta_g \right)^2  ] \end{alignat}  \\
      & = ? \\
      & = ? \\