## Overview🔗

The surfaceInertia utility determines the following properties of a user-supplied surface file:

• inertia tensor for the thin shell or solid body enclosed by the surface;
• principal axes; and
• moments.

## Usage🔗

### Synopsis🔗

surfaceInertia [OPTIONS] <input>


#### Examples

surfaceInertia -referencePoint '(0 0 1)' surface.stl


### Input🔗

#### Arguments

<input>           The input surface file


#### Options

  -case <dir>       Case directory (instead of current directory)
-density <scalar>
Specify density, kg/m3 for solid properties, kg/m2 for
shell properties
-referencePoint <vector>
Inertia relative to this point, not the centre of mass
-shellProperties  Inertia of a thin shell
-doc              Display documentation in browser
-help             Display short help and exit
-help-full        Display full help and exit



No file needed.

No field needed.

### Output🔗

#### Logs

Property Type
Mass of the surface scalar
Centre of mass of the surface vector
Surface area scalar
Inertia tensor around centre of mass tensor
Eigen values - principal moments vector
Eigen vectors - principal axes vectors
Transform tensor from reference state (orientation) tensor

#### Files

Property Description Path Type
axes.obj Writes scaled principal axes at centre of mass of the surface <case>/ obj

No field output.

## Method🔗

The inertia of the surface or the volume is evaluated as follows.

### Shell🔗

The first step is to compute the centre of mass, $$c_m$$:

$c_m = \frac{\sum_{i=1}^{n} | S_{t,i} | c_{t,i}}{\sum_{i=1}^{n} | S_{t,i} |},$

where $$S_t$$ is the triangle area and $$n$$ the number of triangles in the surface.

The tensorial inertia, $$J$$, around the centre of mass determined using:

$J = \sum_{i=1}^{n} J_{t,i},$

where $$J_t$$ is the inertia of a triangle.

### Solid🔗

The calculation follows the procedure from the Geometric Tools library. Further details can be found in [15].

## Further information🔗

Tutorial:

• None

Source code:

History:

• Introduced in version 1.7.0