surfaceInertia

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

Files

No file input required.

Fields

No field input required.

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

Fields

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:

• surfaceInertia
• momentOfInertia

History: Introduced in version 1.7.0