Re: Moment of Inertia for 2D Shapes
- From: hoffmann@xxxxxxxxxxxx
- Date: Mon, 28 Jul 2008 08:58:02 -0700 (PDT)
Björn Olde schrieb:
Hi there,
I need some help to calculate the moment of Inertia of a Shape with N
EdgePoints. I also wasn't able to find the Equation of the moment of
Inertia of a Ellipse.
For the Ellipse I use 1/2m*(rx�+ry�) , I changed the Equation of the
Circle to this but I don't know if it is correct.
But the main Problem I got, is to calculate the Inertia of a Polygon.
On the net I found an Equation:
SUMi = Mi*Ri�
M for the Mass of a Point and R for the Length to the RotationPoint.
But when I calculate this for a Rectangle, I got really different Values
from the Equation 1/12m*(a�+b�) which is the normal Equation to
calculate Inertia of a Rectangle.
Maybe someone can give me a hint or a useful link or an Algorithmus?
Thanks,
Bj�rn Olde
Assumed, your polygon is 'simple', you may
subdivide it into triangles in the xy-plane which share
one corner at the rotation axis z, at x=0 and y=0.
For each triangle with new local coordinates x,y, the
formula for the polar moment of inertia is shown here:
http://www.efunda.com/math/areas/triangle.cfm
The moments for the triangles can be added despite
different local coordinates.
I didn't check the correctness. Search as well by
Moment of Inertia & Triangle & Covariance
Best regards -Gernot Hoffmann
.
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