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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 needed.

Fields

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

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:

History:

  • Introduced in version 1.7.0