[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