This section will help you read the information given in
the Measure Inertia dialog box for Inertia Matrix / G, Inertia Matrix / O,
Inertia Matrix / P and Inertia Matrix / Axis System A.

Moments and Products of 3D Inertia

Iox 
Moment of inertia of the object about the ox axis: 

Ioy 
Moment of inertia of the object about the oy axis: 

Ioz 
Moment of inertia of the object about the oz axis: 

Pxy 
Product of inertia of the object about axes ox and oy: 

Pxz 
Product of inertia of the object about axes ox and oz: 

Pyz 
Product of inertia of the object about axes oy and oz: 

(where M is the mass of the object; units:
kg.m^{2}) 
Moments and Products of 2D Inertia

Iox 
Moment of inertia of the surface about the ox axis: 

Ioy 
Moment of inertia of the surface about the oy axis: 

Pxy 
Product of inertia of the surface about axes ox and oy: 

(where A is the surface; units: m^{4}) 
Matrix of Inertia

3D Inertia:

2D Inertia:



where I is the matrix of inertia of the object with respect
to orthonormal basis Oxyz 
Moments and
Principal Axes
The matrix of inertia being a real matrix (whose
elements consist entirely of real numbers) and a symmetric matrix, there
exists an orthonormal basis of vectors
in
this matrix of inertia.
The principal axes are defined by vectors
and
inertia principal moments are expressed by
Note:
is an orthonormal direct basis. 
Expression in Any Axis System:

I is the matrix of inertia with respect to orthonormal
basis Oxyz.
Huygen's theorem is used to transform the matrix of
inertia:
(parallel axis theorem).
Let I' be the matrix of inertia with respect to orthonormal
basis Pxyz
where 

M = {u,v,w}: transformation matrix from basis (Pxyz) to
basis (Puvw)
TM is the transposed matrix of matrix M.
J is the matrix of inertia with respect to an orthonormal
basis Puvw:
J = TM.I'.M 
Additional Notation Used in Measure
Inertia Command

Ixy = (Pxy) 
Ixz = (Pxz) 
Iyz = (Pyz) 
Note: Since entries for the opposite of the product are
symmetrical, they are given only once in the dialog box. 
IoxG 
Moment of inertia of the object about the ox axis with
respect to the system Gxyz, where G is the center of gravity. 
IoxO 
Moment of inertia of the object about the ox axis with
respect to the system Oxyz, where O is the origin of the document. 
IoxP 
Moment of inertia of the object about the ox axis with
respect to the system Pxyz, where P is a selected point. 
IoxA 
Moment of inertia of the object about the ox axis with
respect to the system Axyz, where A is a selected axis system. 
etc. 
