Hello,
I am trying to find moment of inertia of various random 3D shapes and I have few general questions.
I take very thin 'plates' of the shape, calculate moment of inertia of that area, multiply it by thickness of one 'plate unit', also I add a square distance it is from the origin...
Hmm, yep, I can see that it does not work every n. What I was trying to do in the first place is to make a program which simply sums up my area integrals * increment (e.g. 0.001). If you start with 1/4 of the area, than every increment the equation shrinks and changes R value by 1 increment's...
If I change first boundaries to: from 0 to (R-z) and change equation to:
∫∫|(R-z)^n - y^n|^(1/n) dy dz
It gives good results. Is that valid for every n?
Hmm, what do you think such for such expression then:
Volume = ∫∫( R^n - |y^n| - |z^n|)^(1/n) dy dz (from 0 to R, from 0 to R) ?
I know it does not work but I can't understand why it doesn't.
Hi there,
I am trying to calculate both volume and moment of inertia of shapes which surface coordinates are depicted by following equation:
|xn| + |yn| + |zn| = Rn
When n is 1 it is simple octahedron, when it is 2, it is sphere and then choosing any n, it becomes something else.
I...