from compas.geometry import Point
__all__ = [
'Inertia',
]
[docs]class Inertia():
"""The moments of inertia represent the spatial distribution of mass in a rigid body.
It depends on the mass, size, and shape of a rigid body with units of
[mass * m**2]. The moments of inertia can be expressed as the components of
a symmetric positive-definite 3x3 matrix, with 3 diagonal elements, and 3
unique off-diagonal elements. Each inertia matrix is defined relative to a
coordinate frame or set of axes.
Attributes
----------
inertia_tensor : list of float
A symmetric positive-definite 3x3 matrix:
| ixx ixy ixz |
| ixy iyy iyz |
| ixz iyz izz |
with [ixx, iyy, izz] as the principal moments of inertia and
[ixy, ixz, iyz] as the products of inertia.
mass: float
The mass of the object in kg.
center_of_mass : :class:`Point`
The center of mass of the object in meters.
Examples
--------
>>> inertia = Inertia([[0] * 3] * 3, 1., Point(0.1, 3.1, 4.4))
>>> inertia
Inertia([[0, 0, 0], [0, 0, 0], [0, 0, 0]], 1.0, Point(0.100, 3.100, 4.400))
>>> inertia.principal_moments
[0, 0, 0]
Notes
-----
Assuming uniform mass density, inertial data can be obtained using the
free software MeshLab, refering to this great `tutorial <http://gazebosim.org/tutorials?tut=inertia>`_.
"""
[docs] def __init__(self, inertia_tensor, mass, center_of_mass):
self.inertia_tensor = inertia_tensor
self.mass = mass
self.center_of_mass = Point(*center_of_mass)
@property
def principal_moments(self):
"""Returns the diagonal elements of the inertia tensor [ixx, iyy, izz]
"""
inertia_tensor = self.inertia_tensor
return [inertia_tensor[0][0], inertia_tensor[1][1], inertia_tensor[2][2]]
def __repr__(self):
return "Inertia({!r}, {!r}, {!r})".format(self.inertia_tensor, self.mass, self.center_of_mass)
[docs] @staticmethod
def calculate_inertia_tensor(cls, mesh):
"""Returns the inertia tensor.
"""
raise NotImplementedError