Difference between revisions of "Template:Free surface submerged plate relations"
From WikiWaves
Jump to navigationJump to search| Line 10: | Line 10: | ||
<center> | <center> | ||
<math> | <math> | ||
| − | \int\nolimits_{-d}^{0}\phi_{n}^h(z)\phi_{m}^d(z) d z | + | \int\nolimits_{-d}^{0}\phi_{n}^h(z)\phi_{m}^d(z) d z |
</math> | </math> | ||
</center> | </center> | ||
| Line 16: | Line 16: | ||
<center> | <center> | ||
<math> | <math> | ||
| − | \int\nolimits_{-h}^{-d}\phi_{n}^h(z)\psi_{m}(z) d z | + | \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]
