Compute inertia matrix for simple solids: cube, sphere and cylinder

inertia_matrix.py

#/usr/bin/env python

# Based on:
# http://mathworld.wolfram.com/MomentofInertia.html


def get_cube_inertia_matrix(mass, x, y, z):
    """Given mass and dimensions of a cube return intertia matrix.
    :return: ixx, ixy, ixz, ixy, iyy, iyz, ixz, iyz, izz
    From https://www.wolframalpha.com/input/?i=moment+of+inertia+cube"""
    ixx = (1.0 / 12.0) * (y**2 + z**2) * mass
    iyy = (1.0 / 12.0) * (x**2 + z**2) * mass
    izz = (1.0 / 12.0) * (x**2 + y**2) * mass
    ixy = 0.0
    ixz = 0.0
    iyz = 0.0
    return [[ixx, ixy, ixz], [ixy, iyy, iyz], [ixz, iyz, izz]]


def get_sphere_inertia_matrix(mass, radius):
    """Given mass and radius of a sphere return inertia matrix.
    :return: ixx, ixy, ixz, ixy, iyy, iyz, ixz, iyz, izz
    From https://www.wolframalpha.com/input/?i=inertia+matrix+sphere
     """
    ixx = iyy = izz = (2.0 / 5.0) * radius**2 * mass
    ixy = 0.0
    ixz = 0.0
    iyz = 0.0
    return [[ixx, ixy, ixz], [ixy, iyy, iyz], [ixz, iyz, izz]]


def get_cylinder_inertia_matrix(mass, radius, height):
    """Given mass and radius and height of a cylinder return inertia matrix.
    :return: ixx, ixy, ixz, ixy, iyy, iyz, ixz, iyz, izz
    https://www.wolframalpha.com/input/?i=inertia+matrix+cylinder&rawformassumption=%7B%22C%22,+%22cylinder%22%7D+-%3E+%7B%22Solid%22%7D
     """
    ixx = (1.0 / 12.0) * (3.0 * radius**2 + height**2) * mass
    iyy = (1.0 / 12.0) * (3.0 * radius**2 + height**2) * mass
    izz = (1.0 / 2.0) * radius**2 * mass
    ixy = 0.0
    ixz = 0.0
    iyz = 0.0
    return [[ixx, ixy, ixz], [ixy, iyy, iyz], [ixz, iyz, izz]]

if __name__ == '__main__':
    import sys
    if len(sys.argv) < 2:
        print "Inertia matrix as:"
        print "[[ixx, ixy, ixz], [ixy, iyy, iyz], [ixz, iyz, izz]]"
        print "Cube inertia of cube mass 1.0 and all dimensions 1.0:"
        print get_cube_inertia_matrix(1.0, 1.0, 1.0, 1.0)
        print "Sphere inertia of mass 1.0 and radius 1.0:"
        print get_sphere_inertia_matrix(1.0, 1.0)
        print "Cylinder inertia of mass 1.0 and radius 1.0 and height 1.0:"
        print get_cylinder_inertia_matrix(1.0, 1.0, 1.0)
    elif len(sys.argv) == 3:
        print get_sphere_inertia_matrix(float(sys.argv[1]),
                                  float(sys.argv[2]))
    elif len(sys.argv) == 4:
        print get_cylinder_inertia_matrix(float(sys.argv[1]),
                                    float(sys.argv[2]),
                                    float(sys.argv[3]))
    elif len(sys.argv) == 5:
        print "Cube inertia matrix:"
        print get_cube_inertia_matrix(float(sys.argv[1]),
                                float(sys.argv[2]),
                                float(sys.argv[3]),
                                float(sys.argv[4]))
    else:
        print "Get the inertia matrix of simple shapes."
        print "Usage:"
        print "For a sphere:"
        print sys.argv[0] + " mass radius"
        print "For a cylinder:"
        print sys.argv[0] + " mass radius height"
        print "For a cube:"
        print sys.argv[0] + " mass x y z"
        print "\nFor example:\n" + sys.argv[0] + "1.0 1.0 1.0 1.0"
        print "[[0.16666666666666666, 0.0, 0.0], [0.0, 0.16666666666666666, 0.0], [0.0, 0.0, 0.16666666666666666]]"

Hi,

Thanks for the script and the links!

According to the link you provide, for the computation of the inertia of a cylinder, don't you have a 4* in front of the height for ixx and iyy?

ixx = (1.0 / 12.0) * (3.0 * radius**2 + height**2) * mass -> ixx = (1.0 / 12.0) * (3.0 * radius**2 + 4*height**2) * mass
iyy = (1.0 / 12.0) * (3.0 * radius**2 + height**2) * mass ->  iyy = (1.0 / 12.0) * (3.0 * radius**2 + 4*height**2) * mass

?