Grasshopper

algorithmic modeling for Rhino

# Product of Inertia

Hello,

I am trying to calculate the principal axis of inertia of a surface. There is a set of equations by which if you know the inertia about two orthogonal axis and the product of inertia about these two axis, you can calculate the principal moment of inertia and the axes of the principal moment of inertia.

Grasshopper includes the [Area Moment] component which gives the Inertia around the centroid of the axis about the x, y, z world axis. But this component doesn't output the product of inertia. Does someone have a VB script that could help me? I've also read this discussion, but I don't know how to make a component from the Rhino SDK.

One notice for the developers (David). In the [Area Moment] and the [Volume Moment] components, the tooltip of the [I] output says "Moment of inertia around the centroid", but it does not specify the orientation of the axis about which they are calculated. I think they are the X,Y,Z world axis centered on the centroid of the surface or body. I think this should be worth mentioning on the info tooltip.

Finally I think that the product of inertia would make a nice improvement to Grasshopper default components, because it would allow one easily calculate the "main" directions of a shape or body.

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Well I was able to edit David's VB and finally obtain the principal axes of a 2D shape. It's useful if you want to orient a piece like for printing or laser cutting.

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Very nice Jesus!

Thank you.

Thanks djordje!

I was actually surprised that this wasn't already covered in this community.

Hi Jesus,

Im looking to simulate the rolling action in GH. using Kangaroo II. do you think that moment of Inertia definition from you might solve the problem ?

this effekt is what I am looking for. and would like to apply that on rigid bodies in Kangaroo.

https://javalab.org/en/moment_of_inertia_en/

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