The Box component models a homogeneous rigid body along a given axial vector with a rectangular cross section. Based on the properties, i.e., axial unit vector, length, height, width, and density, the center of mass, mass, and moments of inertia are calculated for this rigid body. Box visualization is a simple cuboid.

Box length (L) is always along the specified axial unit vector (e_axis). Unit vectors for width (W) and height (H) are defined according to Figure 1. The sequence depends on whether or not the Rotate 90 degrees option is checked (true).

Figure 1: Order of L, W, and H follows above diagrams. Rotate 90 degrees option is unchecked (false) for the left sequence and checked (true) for the right one.

Note that the rotate 90 degrees option just rotates the box cross section. Regardless of this option, the orientation of the end frames and additional frames remains the same. Translation vectors of $L \mathrm{e\_\_axis}$ and $\frac{L}{2} \mathrm{e\_\_axis}$ w.r.t. frame_a defines the frame_b and the center of mass frame respectively. Moreover, each additional frame is defined by translating from frame_a along the vector $\mathrm{L\_\_add}\left[i\right] \mathrm{e\_\_axis}$. This is illustrated in the following figure.

Figure 2: Orientation of end frames and an additional frame with $\mathrm{L\_\_add} \=\left[\frac{L}{2}\right]$for a box along the x-axis

Box mass is calculated as

$m\=\mathrm{\ρ} L\cdot \left(H W-\mathrm{H\_\_i}\mathrm{W\_\_i}\right)$

where the box material density, ρ, can be defined using the "Select density" parameter. This parameter lets the user either enter a value or select among predefined material densities.

Figure 3: Different options for the "Select density" parameter

Assuming the default direction of $\left[1\,0\,0\right]$ for the e_axis and that the Rotate 90 degrees option is unchecked (false), the moments of inertia expressed from the center of mass frame (frame_a) are

$\mathrm{I\_\_xx}\=\frac{\mathrm{\ρ} L}{12}\cdot \left(H W\cdot \left(H{ }^2\+W{ }^2\right)-H\mathrm{\_\_i} \mathrm{W\_\_i}\cdot \left(\mathrm{H\_\_i}{ }^2\+\mathrm{W\_\_i}{ }^2\right)\right)$

$\mathrm{I\_\_yy}\=\frac{\mathrm{\rho } L}{12}\cdot \left(\mathrm{WL}\cdot \left(W{ }^2\+L{ }^2\right)-H\mathrm{`\; `\_\_i} \mathrm{W\_\_i}\cdot \left(\mathrm{W\_\_i}{ }^2\+L{ }^2\right)\right)$

$\mathrm{I\_\_zz}\=\frac{\mathrm{\rho } L}{12}\cdot \left(H L\cdot \left(H{ }^2\+L{ }^2\right)-H\mathrm{`\; `\_\_i} \mathrm{W\_\_i}\cdot \left(\mathrm{H\_\_i}{ }^2\+L{ }^2\right)\right)$

The right-hand side of these equations will interchange if another axial unit vector is specified or the Rotate 90 degrees parameter is true.