Difference between revisions of "Template:Free surface submerged plate relations"

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<center>
 
<center>
 
<math>
 
<math>
\int\nolimits_{-d}^{0}\phi_{n}^h(z)\phi_{m}^d(z) d z=B_{mn}
+
\int\nolimits_{-d}^{0}\phi_{n}^h(z)\phi_{m}^d(z) d z
 
</math>
 
</math>
 
</center>
 
</center>
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<center>
 
<center>
 
<math>
 
<math>
\int\nolimits_{-h}^{-d}\phi_{n}^h(z)\psi_{m}(z) d z=B_{mn}
+
\int\nolimits_{-h}^{-d}\phi_{n}^h(z)\psi_{m}(z) d z
 
</math>
 
</math>
 
</center>
 
</center>

Revision as of 11:16, 7 September 2008

Inner product between free surface and submerged plate modes

We define

[math]\displaystyle{ \int\nolimits_{-d}^{0}\phi_{n}^h(z)\chi_{m}^d(z) d z=B_{mn} }[/math]

where [math]\displaystyle{ B_{mn} }[/math] is either

[math]\displaystyle{ \int\nolimits_{-d}^{0}\phi_{n}^h(z)\phi_{m}^d(z) d z }[/math]

or

[math]\displaystyle{ \int\nolimits_{-h}^{-d}\phi_{n}^h(z)\psi_{m}(z) d z }[/math]