Second Moment of Inertia using Green's Theorem
Green's Theorem:
double intergral ( curl vector(F) dA ) = closed integral ( vector(F) dot vector(ds) )
What I need is double integral ( x^2 + y^2 dA ), right?
Knowing that vector(F) = <F1, F2>.. and applying green's theorem to this problem we get: dF2/dy - dF1/x = x^2 + y^2. I just chose F1 = 0. So F2 = x^2*y + y^3/3.
My areas are polygonal, so I am just going to parameterize the boundaries into segments and from there it should go alright.
So my question is: Is my work correct?
You're not going to get too far using two dimensional vectors with the curl operator. Unless, of course, you want to get an answer that has only a Z component.
Or were you just being brief?
Or were you just being brief?
What rotation/deformation.. If u're talking about curl operator.. Well it's a differential operator. curl( F1, F2 ) = dF2/dx - dF1/dy
Ah, no. Your topic is about the second moment of inertia (aka second moment of area) but the math looks like it's for the moment of inertia. In either case, can I assume the axis of rotation is k?
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