Jump to content
  • Advertisement


This topic is now archived and is closed to further replies.


inertia tensor matrix for ensemble of particles.

This topic is 5911 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

Could somebody tell me how to do this or show me a link? a rigid body has an inertia tensor matrix calculatable from the objects mass. my object is an ensemble of particles with mass. how do i calculate its inertia matrix?

Share this post

Link to post
Share on other sites
oh man, still no replies? well the truth is, it''s because finding the inertia tensor for complex objects is difficult. i''m not sure what your "ensemble" most closely resembles, but you should be able to find formulae for primitives like spheres and boxes.


Share this post

Link to post
Share on other sites
Its actually quite simple to calculate the inertia tensor for a cloud of spherical particles with mass:

Let (Xo, Yo, Zo) be the point about which you want to calculate the inertias. Then, here''s the pseudocode

float Ixx = 0., Iyy = 0., Izz = 0., Ixy = 0., Ixz = 0.;
float Iyz = 0., mass = 0.
Particle *p = all the particles;

for (int i = 0; i < numparticles; i++)
mass += p.mass;
Ixx += p[i].mass*(p[i].y*p[i].y + p[i].z*p[i].z);
Iyy += p[i].mass*(p[i].x*p[i].x + p[i].z*p[i].z);
Izz += p[i].mass*(p[i].x*p[i].x + p[i].y*p[i].y);
Ixy += p[i].mass*(p[i].x*p[i].y);
Ixz += p[i].mass*(p[i].x*p[i].z);
Iyz += p[i].mass*(p[i].y*p[i].z);

When you''re done, the inertia tensor will be:

[ Ixx Ixy Ixz ]
IT = | Iyx Iyy Iyz |
[ Izx Izy Izz ]

And you also have the total mass of the system.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

Share this post

Link to post
Share on other sites
i stand corrected. Bourg also has this method of calculating the tensor in his Physics for Game Developers book.


Share this post

Link to post
Share on other sites

  • Advertisement

Important Information

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

We are the game development community.

Whether you are an indie, hobbyist, AAA developer, or just trying to learn, GameDev.net is the place for you to learn, share, and connect with the games industry. Learn more About Us or sign up!

Sign me up!