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# the right way to represent inverse inertia tensor

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5 replies to this topic

### #1Irlan Robson  Members

Posted 11 February 2013 - 08:22 AM

float Ix, Iy, Iz;

Ix = Iy = Iz = 0.4f * mass * radius * radius; //solid sphere

inertia.m11 = Ix;            inertia.m12 = 0;        inertia.m13 = 0;
inertia.m21 = 0;            inertia.m22 = Iy;        inertia.m23 = 0;
inertia.m31 = 0;            inertia.m32 = 0;        inertia.m33 = Iz;

b_inertia = m_inertia_inverse = inertia.inverse();
float inverseInertia = 1.0f / Ix;

i'm doing this way and it's giving me problems... are you agree that is the right way??

### #2Dirk Gregorius  Members

Posted 11 February 2013 - 10:29 AM

The inverse of inertia tensor in 3D is an inertia tensor itself. The example of the sphere is missleading since it is some scalar factor times the identity matrix.

### #3Irlan Robson  Members

Posted 11 February 2013 - 11:28 AM

oh... then, i don't need to do: b_inertia = m_inertia_inverse = inertia.inverse(); right??

Edited by irlanrobson, 11 February 2013 - 11:29 AM.

### #4EWClay  Members

Posted 11 February 2013 - 12:35 PM

The inverse of inertia tensor in 3D is an inertia tensor itself. The example of the sphere is missleading since it is some scalar factor times the identity matrix.

Not sure what you are saying there. The units are different and a general inertia tensor is not equal to its inverse, and neither is it for a sphere.

Nothing looks obviously wrong with the matrix above.

### #5luca-deltodesco  Members

Posted 11 February 2013 - 12:51 PM

inverse_inertia = inertia.inverse();

Anyways, if it aids:

By choosing the correct coordinate system for the object (For basic objects, the obvious one), you can always diagonalise the inertia tensor, and so it, and its inverse can be stored in a vector instead of a matrix, and then the inverse is just the component wise inverse:

(Ix, Iy, Iz)^-1 = (1/Ix, 1/Iy, 1/Iz)

Edited by luca-deltodesco, 11 February 2013 - 12:57 PM.

### #6Irlan Robson  Members

Posted 11 February 2013 - 01:25 PM

oh

inverse_inertia = inertia.inverse();

Anyways, if it aids:

By choosing the correct coordinate system for the object (For basic objects, the obvious one), you can always diagonalise the inertia tensor, and so it, and its inverse can be stored in a vector instead of a matrix, and then the inverse is just the component wise inverse:

(Ix, Iy, Iz)^-1 = (1/Ix, 1/Iy, 1/Iz)

hm... so i can use vectors .... or i can use   float inverseInertia = 1.0f / Ix; instead of vectors and do the multiplication between them...

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