RCAIDE.Library.Methods.Mass_Properties.Moment_of_Inertia.compute_rounded_end_cylinder_moment_of_inertia

compute_rounded_end_cylinder_moment_of_inertia#

compute_rounded_end_cylinder_moment_of_inertia(component, outer_length, outer_radius, inner_length, inner_radius, center_of_gravity=array([[0, 0, 0]]), fuel_tank=False)[source]#

Computes the moment of inertia tensor for a hollow rounded-end cylinder.

Parameters:

  • origin (numpy.ndarray) – Origin coordinates of the component [m]

  • mass (float) – Total mass of the cylinder [kg]

  • outer_length (float) – Length of the outer cylinder [m]

  • outer_radius (float) – Radius of the outer cylinder [m]

  • inner_length (float, optional) – Length of the inner cylinder (for hollow cylinder) [m], default is 0

  • inner_radius (float, optional) – Radius of the inner cylinder (for hollow cylinder) [m], default is 0

  • center_of_gravity (numpy.ndarray, optional) – Global center of gravity coordinates [m], default is [0,0,0]

Returns:

  • I_global (numpy.ndarray) – Moment of inertia tensor in global coordinate system [kg⋅m²] Shape: (3, 3) matrix

  • mass (float) – Mass of the cylinder [kg]

Notes

This function computes the moment of inertia tensor for a hollow rounded-end cylinder using the parallel axis theorem to transform from local to global coordinate systems. The cylinder consists of a cylindrical section with hemispherical end caps.

Major Assumptions

  • Cylinder has constant density throughout

  • Cylinder axis is aligned with the x-axis

  • Rounded ends are perfect hemispheres

  • Parallel axis theorem is valid for the transformation

  • Point mass approximation for zero radius/length cases

Theory

The volume of a rounded-end cylinder is: \(V = V_{cylinder} + V_{hemispheres} = \pi r^2 L + \frac{4}{3}\pi r^3\)

For a hollow cylinder: \(V_{total} = V_{outer} - V_{inner}\)

The density is calculated as: \(\rho = \frac{m}{V}\)

The parallel axis theorem transforms the moment of inertia: \(I_{global} = I_{local} + m(\|\vec{s}\|^2 \mathbf{I} - \vec{s} \vec{s}^T)\)

where \(\vec{s}\) is the vector from the component origin to the global center of gravity.