## Documentation Center |

On this page… |
---|

The inertia tensor is a 3×3 matrix that governs the rotational behavior of a rigid body. This matrix is symmetric: elements with reciprocal indices have the same value. That is:

I_{xy}=I_{yx},
I_{yz}=I_{zy}, I_{zx}=I_{xz}

Because the inertia tensor is symmetric, it requires only six elements. Three are the moments of inertia and three are the products of inertia. The complete inertia tensor has the form:

You can specify the inertia tensor manually, using one of two
blocks: Solid and Inertia.
To do this, in the block dialog box select `Custom` from
the **Inertia** > **Type** drop-down menu. In the new set of parameters that appears,
specify the inertia tensor in terms of the moments and products of
inertia.

The moments of inertia are the three diagonal terms of the inertia tensor:

In the **Moments
of Inertia** dialog box parameter, enter the three diagonal
elements as a row vector. Enter the elements in the order [I_{xx},
I_{yy}, I_{zz}].
These are the moments of inertia of the solid with respect to a frame
whose axes align with the block reference frame, and whose origin
coincides with the solid center of mass.

The products of inertia are the three unique off-diagonal elements. Because the inertia tensor is symmetric, each off-diagonal element appears twice in the matrix.

In the **Products
of Inertia** dialog box parameter, enter the three unique
off-diagonal elements. Enter the elements in the order [I_{yz},
I_{zx}, I_{xy}].
One easy way to remember the element order is to think of the missing
subscript component: x, y, and z respectively. The elements are the
products of inertia of the solid with respect to a frame whose axes
align with the block reference frame, and whose origin coincides with
the solid center of mass.

Was this topic helpful?