The Disk component models a homogeneous disk-like rigid body along a given axis with a predefined density. Based on the properties, i.e., axial unit vector, radius, and density, the center of mass, total mass, and moments of inertia are calculated for this rigid body. Although Disk and Cylinder components share similarities, Disk is preferred when length/thickness is insignificant compared to radius.

The arrays $\mathrm{R\_\_add}$and $\mathrm{\θ\_\_add}$ should have the same length. Each additional frame is defined by rotating frame_a around the axial vector an angle $\mathrm{\θ\_\_add}\left[i\right]$ and then translating along the reference axis by $\mathrm{L\_\_add}\left[i\right]$. The reference axis is the next local axis after the e_axis (e.g., if e_axis is y, the reference axis is z). Figure 1 illustrates this process.

Figure 1: The axial unit vector (e_axis) for this disk is [0,1,0]. Additional frame was added by defining $\mathrm{L\_\_add} \= \left[\frac{R}{2}\,R\right]$and $\mathrm{\θ\_\_add}\=\left[45\,180\right] \mathrm{deg}$. Both of these frames lie on the plane defined by the normal vector of e_axis and passing through the center of mass.

Disk mass is calculated as

$m\=\mathrm{\rho } \mathrm{\pi }\cdot \left(R^2-{\mathrm{R\_\_i}}^2\right) T$

where the disk 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 2: Different options for the "Select density" parameter

Assuming the default direction of $\left[1\,0\,0\right]$ for the e_axis, the moments of inertia expressed from the center of mass frame (frame_a) are

$\mathrm{I\_\_xx}\=\frac{1}{2} m\cdot \left(R^2\+{\mathrm{R\_\_i}}^2\right)$

$\mathrm{I\_\_yy}\=\frac{1}{12} m\cdot \left(3\left(R^2\+{\mathrm{R\_\_i}}^2\right)\+T{ }^2\right)$

$\mathrm{I\_\_zz}\=\mathrm{I\_\_yy}$

The right-hand side of these equations will interchange if another axial unit vector is specified.