def shift_com_inertia_3x3(mass,
com,
inertia_com,
ref_point=mathutils.Vector((0.0, ) * 3)):
"""Shifts the center
This code was adapted from an implementation generously provided by Bertold Bongardt.
shift inertia matrix, steiner theorem / parallel axis theorem, private method
- without changing the orientation -
see SCISIC B.12 or featherstone 2.63, but not Selig (sign swap, not COG)
c = COG - O
I_O = I_COG + m · c× (c× )T
changed the formula to (Wikipedia):
\mathbf{J} = \mathbf{I} + m \left[\left(\mathbf{R} \cdot \mathbf{R}\right) \mathbf{E}_{3} - \mathbf{R} \otimes \mathbf{R} \right],
This was necessary as previous calculations founded on math libraries of cad2sim.
"""
c = com - ref_point # difference vector
c_outer = gUtils.outerProduct(c, c)
inertia_ref = inertia_com + mass * (
c.dot(c) * mathutils.Matrix.Identity(3) - c_outer)
return inertia_ref
def shift_cog_inertia_3x3(mass,
cog,
inertia_cog,
ref_point=mathutils.Vector((0.0, ) * 3)):
"""
shift inertia matrix, steiner theorem / parallel axis theorem, private method
- without changing the orientation -
see SCISIC B.12 or featherstone 2.63, but not Selig (sign swap, not COG)
c = COG - O
I_O = I_COG + m · c× (c× )T
changed the formula to (Wikipedia):
\mathbf{J} = \mathbf{I} + m \left[\left(\mathbf{R} \cdot \mathbf{R}\right) \mathbf{E}_{3} - \mathbf{R} \otimes \mathbf{R} \right],
This was necessary as previous calculations founded on math libraries of cad2sim.
"""
# diff_vec
c = cog - ref_point
c_outer = generalUtils.outerProduct(c, c)
inertia_ref = inertia_cog + mass * (
c.dot(c) * mathutils.Matrix.Identity(3) - c_outer)
return inertia_ref
def shift_cog_inertia_3x3(mass, cog, inertia_cog, ref_point=mathutils.Vector((0.0,)*3)):
"""
shift inertia matrix, steiner theorem / parallel axis theorem, private method
- without changing the orientation -
see SCISIC B.12 or featherstone 2.63, but not Selig (sign swap, not COG)
c = COG - O
I_O = I_COG + m · c× (c× )T
changed the formula to (Wikipedia):
\mathbf{J} = \mathbf{I} + m \left[\left(\mathbf{R} \cdot \mathbf{R}\right) \mathbf{E}_{3} - \mathbf{R} \otimes \mathbf{R} \right],
This was necessary as previous calculations founded on math libraries of cad2sim.
"""
# diff_vec
c = cog - ref_point
c_outer = generalUtils.outerProduct(c, c)
inertia_ref = inertia_cog + mass * (c.dot(c) * mathutils.Matrix.Identity(3) - c_outer)
return inertia_ref
def shift_com_inertia_3x3(mass, com, inertia_com, ref_point=mathutils.Vector((0.0,) * 3)):
"""Shifts the center of mass of a 3x3 inertia.
This code was adapted from an implementation generously provided by Bertold Bongardt.
TODO cleanup docstring
shift inertia matrix, steiner theorem / parallel axis theorem, private method
- without changing the orientation -
see SCISIC B.12 or featherstone 2.63, but not Selig (sign swap, not COG)
| c = COG - O
| I_O = I_COG + m · c× (c× )T
|
| changed the formula to (Wikipedia):
| \\mathbf{J} = \\mathbf{I} + m \\left[\\left(\\mathbf{R} \\cdot \\mathbf{R}\\right)
| \\mathbf{E}_{3} - \\mathbf{R} \\otimes \\mathbf{R} \\right],
This was necessary as previous calculations founded on math libraries of cad2sim.
Args:
mass:
com:
inertia_com:
ref_point: (Default value = mathutils.Vector((0.0)
) * 3):
Returns:
"""
c = com - ref_point # difference vector
c_outer = gUtils.outerProduct(c, c)
inertia_ref = inertia_com + mass * (c.dot(c) * mathutils.Matrix.Identity(3) - c_outer)
return inertia_ref