U Zʹj@sjddlmZddlmZmZmZmZddlmZdddgZ d ddZ ddZ Gd ddedd d gZ d S))sympify)PointDyadicReferenceFrameouter) namedtupleinertiainertia_of_point_massInertiacCst|tstdt|t|t|}}}t|t|t|}}}|t|j|j|t|j|j|t|j|j|t|j|j|t|j|j|t|j|j|t|j|j|t|j|j|t|j|jS)a~Simple 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)frameixxiyyizzixyiyzizxr^/var/www/html/bwave/python/venv/lib/python3.8/site-packages/sympy/physics/mechanics/inertia.pyrs&% "cCsB|t|j|jt|j|jt|j|j||t||S)aOInertia 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)ZmassZpos_vecrrrrr 8s   csFeZdZdZfddZed ddZddZd d ZeZ eZ Z S) r ayInertia 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) csRt|trt|tr||}}t|ts0tdt|tsBtdt|||S)Nz'Reference point should be of type Pointz-Inertia value should be expressed as a Dyadic)r rrr super__new__)clsdyadicpoint __class__rrr{s   zInertia.__new__rc Cs|t||||||||S)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) rrrrrrrrrrrrfrom_inertia_scalarss3zInertia.from_inertia_scalarscCs"td|jjd|jjddS)Nz$unsupported operand type(s) for +: '' and ''r r __name__selfotherrrr__add__szInertia.__add__cCs"td|jjd|jjddS)Nz$unsupported operand type(s) for *: 'r"r#r$r&rrr__mul__szInertia.__mul__)rrr) r% __module__ __qualname____doc__r classmethodr!r)r*__radd____rmul__ __classcell__rrrrr Ys!  4rrN)rrr) ZsympyrZsympy.physics.vectorrrrr collectionsr__all__rr r rrrrs    0!