Jump to content
  • Advertisement
Sign in to follow this  

Second Moment of Inertia using Green's Theorem

This topic is 3848 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

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?

Share this post


Link to post
Share on other sites
Advertisement
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?

Share this post


Link to post
Share on other sites
What rotation/deformation.. If u're talking about curl operator.. Well it's a differential operator. curl( F1, F2 ) = dF2/dx - dF1/dy

Share this post


Link to post
Share on other sites
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?

Share this post


Link to post
Share on other sites
Yes..
But in later stages in code, there's gonna be some finite element stuff, so let's build on the simple stuff first, and then I'll see how to deal with the changing stuff.

Share this post


Link to post
Share on other sites
Sign in to follow this  

  • Advertisement
×

Important Information

By using GameDev.net, you agree to our community Guidelines, Terms of Use, and Privacy Policy.

Participate in the game development conversation and more when you create an account on GameDev.net!

Sign me up!