# trimesh.inertia module¶

## inertia.py¶

Functions for dealing with inertia tensors.

Results validated against known geometries and checked for internal consistency.

Functions

 `cylinder_inertia`(mass, radius, height[, …]) Return the inertia tensor of a cylinder. `principal_axis`(inertia) Find the principal components and principal axis of inertia from the inertia tensor. Check whether a mesh has radial symmetry. `sphere_inertia`(mass, radius) Return the inertia tensor of a sphere. `transform_inertia`(transform, inertia_tensor) Transform an inertia tensor to a new frame.
`trimesh.inertia.``cylinder_inertia`(mass, radius, height, transform=None)

Return the inertia tensor of a cylinder.

Parameters
• mass (float) – Mass of cylinder

• height (float) – Height of cylinder

• transform ((4, 4) float) – Transformation of cylinder

Returns

inertia – Inertia tensor

Return type

(3, 3) float

`trimesh.inertia.``principal_axis`(inertia)

Find the principal components and principal axis of inertia from the inertia tensor.

Parameters

inertia ((3, 3) float) – Inertia tensor

Returns

• components ((3,) float) – Principal components of inertia

• vectors ((3, 3) float) – Row vectors pointing along the principal axes of inertia

`trimesh.inertia.``radial_symmetry`(mesh)

Check whether a mesh has radial symmetry.

Returns

• symmetry (None or str) – None No rotational symmetry ‘radial’ Symmetric around an axis ‘spherical’ Symmetric around a point

• axis (None or (3,) float) – Rotation axis or point

• section (None or (3, 2) float) – If radial symmetry provide vectors to get cross section

`trimesh.inertia.``sphere_inertia`(mass, radius)

Return the inertia tensor of a sphere.

Parameters
• mass (float) – Mass of sphere

Returns

inertia – Inertia tensor

Return type

(3, 3) float

`trimesh.inertia.``transform_inertia`(transform, inertia_tensor)

Transform an inertia tensor to a new frame.

More details in OCW PDF: MIT16_07F09_Lec26.pdf

Parameters
• transform ((3, 3) or (4, 4) float) – Transformation matrix

• inertia_tensor ((3, 3) float) – Inertia tensor

Returns

transformed – Inertia tensor in new frame

Return type

(3, 3) float