+ i v^RIHt^RIHtHtHtHt^RIHt.R Ot R Rlt Rt !RR]!RRR .44t R #) )sympify)PointDyadicReferenceFrameouter) namedtupleInertiac\V\4'g \R4h\V4\V4\V4r2p\V4\V4\V4repV\ VP VP 4,V\ VP VP 4,,V\ VP VP4,,V\ VP VP 4,,V\ VP VP 4,,V\ VP VP4,,V\ VPVP 4,,V\ VPVP 4,,V\ VPVP4,,#)aSimple way to create inertia Dyadic object. Explanation =========== Creates an inertia Dyadic based on the given tensor values and a body-fixed reference frame. Parameters ========== frame : ReferenceFrame The frame the inertia is defined in. ixx : Sympifyable The xx element in the inertia dyadic. iyy : Sympifyable The yy element in the inertia dyadic. izz : Sympifyable The zz element in the inertia dyadic. ixy : Sympifyable The xy element in the inertia dyadic. iyz : Sympifyable The yz element in the inertia dyadic. izx : Sympifyable The zx element in the inertia dyadic. Examples ======== >>> from sympy.physics.mechanics import ReferenceFrame, inertia >>> N = ReferenceFrame('N') >>> inertia(N, 1, 2, 3) (N.x|N.x) + 2*(N.y|N.y) + 3*(N.z|N.z) z%Need to define the inertia in a frame) isinstancer TypeErrorrrxyz)frameixxiyyizzixyiyzizxs&&&&&&&]/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/physics/mechanics/inertia.pyinertiarsNJ e^ , ,?@@CL'#, cCCL'#, cC egguww' '#eEGGUWW.E*E E egguww' ' (*-eEGGUWW.E*E F egguww' ' (*-eEGGUWW.E*E F egguww' ' (+.eEGGUWW.E*E F egguww' '  ()c0V\VPVP4\VPVP4,\VPVP4,VP V4,\W4, ,#)aInertia dyadic of a point mass relative to point O. Parameters ========== mass : Sympifyable Mass of the point mass pos_vec : Vector Position from point O to point mass frame : ReferenceFrame Reference frame to express the dyadic in Examples ======== >>> from sympy import symbols >>> from sympy.physics.mechanics import ReferenceFrame, inertia_of_point_mass >>> N = ReferenceFrame('N') >>> r, m = symbols('r m') >>> px = r * N.x >>> inertia_of_point_mass(m, px, N) m*r**2*(N.y|N.y) + m*r**2*(N.z|N.z) )rr rrdot)masspos_vecrs&&&rinertia_of_point_massr8ss4  uww uww  ! uww  ! W  "'w!8 9 ::rcbaa]tRt^YtoRtRtV3Rlt]RRl4tRt Rt ] t ] t Rt VtV;t#)r aInertia object consisting of a Dyadic and a Point of reference. Explanation =========== This is a simple class to store the Point and Dyadic, belonging to an inertia. Attributes ========== dyadic : Dyadic The dyadic of the inertia. point : Point The reference point of the inertia. Examples ======== >>> from sympy.physics.mechanics import ReferenceFrame, Point, Inertia >>> N = ReferenceFrame('N') >>> Po = Point('Po') >>> Inertia(N.x.outer(N.x) + N.y.outer(N.y) + N.z.outer(N.z), Po) ((N.x|N.x) + (N.y|N.y) + (N.z|N.z), Po) In the example above the Dyadic was created manually, one can however also use the ``inertia`` function for this or the class method ``from_tensor`` as shown below. >>> Inertia.from_inertia_scalars(Po, N, 1, 1, 1) ((N.x|N.x) + (N.y|N.y) + (N.z|N.z), Po) c<\V\4'd\V\4'dYr\V\4'g \R4h\V\4'g \R4h\SV`WV4#)z'Reference point should be of type Pointz-Inertia value should be expressed as a Dyadic)r rrr super__new__)clsdyadicpoint __class__s&&&rr"Inertia.__new__}sd fe $ $E6)B)B"6%''EF F&&))KL LwsE22rc  ,V!\W#WEWgV4V4#)aSimple way to create an Inertia object based on the tensor values. Explanation =========== This class method uses the :func`~.inertia` to create the Dyadic based on the tensor values. Parameters ========== point : Point The reference point of the inertia. frame : ReferenceFrame The frame the inertia is defined in. ixx : Sympifyable The xx element in the inertia dyadic. iyy : Sympifyable The yy element in the inertia dyadic. izz : Sympifyable The zz element in the inertia dyadic. ixy : Sympifyable The xy element in the inertia dyadic. iyz : Sympifyable The yz element in the inertia dyadic. izx : Sympifyable The zx element in the inertia dyadic. Examples ======== >>> from sympy import symbols >>> from sympy.physics.mechanics import ReferenceFrame, Point, Inertia >>> ixx, iyy, izz, ixy, iyz, izx = symbols('ixx iyy izz ixy iyz izx') >>> N = ReferenceFrame('N') >>> P = Point('P') >>> I = Inertia.from_inertia_scalars(P, N, ixx, iyy, izz, ixy, iyz, izx) The tensor values can easily be seen when converting the dyadic to a matrix. >>> I.dyadic.to_matrix(N) Matrix([ [ixx, ixy, izx], [ixy, iyy, iyz], [izx, iyz, izz]]) )r) r#r%rrrrrrrs &&&&&&&&&rfrom_inertia_scalarsInertia.from_inertia_scalarssf75s3?GGrcv\RVPP RVPP R24h)z$unsupported operand type(s) for +: '' and ''r r&__name__selfothers&&r__add__Inertia.__add__@ NN3345!OO445Q89 9rcv\RVPP RVPP R24h)z$unsupported operand type(s) for *: 'r,r-r.r0s&&r__mul__Inertia.__mul__r5rrrr)r/ __module__ __qualname____firstlineno____doc__ __slots__r" classmethodr)r3r7__radd____rmul____static_attributes____classdictcell__ __classcell__)r& __classdict__s@@rr r YsF BI32H2Hh9 9 HHHrr$r%N)rrr r:) sympyrsympy.physics.vectorrrrr collectionsr__all__rrr r9rrrKs<EE" 9-)`:BnjXw$78nr