[ODE] Inertia question

Mattias Fagerlund mattias at cambrianlabs.com
Sat Feb 15 02:35:02 2003


Hi, I have an inertia / pressure question that someone here might be 
able to help me with. It's not really ODE related, but it might become 
ODE related, if I get this working. I'm trying to work out hydrostatic 
forces on a 3d mesh fully (trivial) or partially (non trivial) submerged 
in a liquid.

The center of pressure on a submerted plane surface is located at;

Ycp = center of pressure
Yc = center of surface along Y axis
Xc = center of surface along X axis
A = area of surface
Ixc = moment of inertia around horizontal centroid axis

Ycp = Ixc/(Yc * A) + Yc (eq 1)

The Ixy of a submerged triangle appears to be 
( see http://www.efunda.com/math/areas/triangle.cfm )
b = width of triangle
a = distance from y axis to top vertex
h = height of triangle
Ixc = moment of inertia around horizontal centroid axis

Ixc = b*h^3 / 36 (eq 2)

Now, all references I've found seem to compute either Xcp or Ycp, but 
never both. What's worse, the moment of inertia formula I've found 
always show the triangle with the base paralell to the x axis. My 
triangles are rarely paralell to the x axis. Is the moment of inertia 
formula still correct for my triangles, or do I have to transform it 
somehow? What would "h" be in eq 2 for such a triangle?

Please advice, over.

cheers,
m