ó ¡¼™\c@snddlmZddlmZmZmZmZddlmZm Z dgZ deefd„ƒYZ dS(iÿÿÿÿ(tSymbol(t RigidBodytParticletReferenceFrametinertia(tPointtVectortBodycBs8eZdZddddd„Zdd„Zd„ZRS(s- Body is a common representation of either a RigidBody or a Particle SymPy object depending on what is passed in during initialization. If a mass is passed in and central_inertia is left as None, the Particle object is created. Otherwise a RigidBody object will be created. The attributes that Body possesses will be the same as a Particle instance or a Rigid Body instance depending on which was created. Additional attributes are listed below. Attributes ========== name : string The body's name masscenter : Point The point which represents the center of mass of the rigid body frame : ReferenceFrame The reference frame which the body is fixed in mass : Sympifyable The body's mass inertia : (Dyadic, Point) The body's inertia around its center of mass. This attribute is specific to the rigid body form of Body and is left undefined for the Particle form loads : iterable This list contains information on the different loads acting on the Body. Forces are listed as a (point, vector) tuple and torques are listed as (reference frame, vector) tuples. Parameters ========== name : String Defines the name of the body. It is used as the base for defining body specific properties. masscenter : Point, optional A point that represents the center of mass of the body or particle. If no point is given, a point is generated. mass : Sympifyable, optional A Sympifyable object which represents the mass of the body. If no mass is passed, one is generated. frame : ReferenceFrame, optional The ReferenceFrame that represents the reference frame of the body. If no frame is given, a frame is generated. central_inertia : Dyadic, optional Central inertia dyadic of the body. If none is passed while creating RigidBody, a default inertia is generated. Examples ======== Default behaviour. This results in the creation of a RigidBody object for which the mass, mass center, frame and inertia attributes are given default values. :: >>> from sympy.physics.mechanics import Body >>> body = Body('name_of_body') This next example demonstrates the code required to specify all of the values of the Body object. Note this will also create a RigidBody version of the Body object. :: >>> from sympy import Symbol >>> from sympy.physics.mechanics import ReferenceFrame, Point, inertia >>> from sympy.physics.mechanics import Body >>> mass = Symbol('mass') >>> masscenter = Point('masscenter') >>> frame = ReferenceFrame('frame') >>> ixx = Symbol('ixx') >>> body_inertia = inertia(frame, ixx, 0, 0) >>> body = Body('name_of_body', masscenter, mass, frame, body_inertia) The minimal code required to create a Particle version of the Body object involves simply passing in a name and a mass. :: >>> from sympy import Symbol >>> from sympy.physics.mechanics import Body >>> mass = Symbol('mass') >>> body = Body('name_of_body', mass=mass) The Particle version of the Body object can also receive a masscenter point and a reference frame, just not an inertia. cCs“||_g|_|dkr1t|dƒ}n|dkrPt|dƒ}n|dkrï|dkrït|dƒ}t|dƒ}t|dƒ}t|dƒ} t|dƒ} t|dƒ} t||||| | | ƒ|f} n ||f} |dkrt|d ƒ} n|} |j|d ƒ|dkrs|dk rs||_||_ t j |||| ƒnt j ||||| | ƒdS( Nt_framet _masscentert_ixxt_iyyt_izzt_izxt_ixyt_iyzt_massi( tnametloadstNoneRRRRtset_veltframet masscenterRt__init__R(tselfRRtmassRtcentral_inertiatixxtiyytizztizxtixytiyzt_inertiaR((s;lib/python2.7/site-packages/sympy/physics/mechanics/body.pyR_s2         cCsnt|tƒs6|dkr'|j}q6tdƒ‚nt|tƒsTtdƒ‚n|jj||fƒdS(sà Adds a force to a point (center of mass by default) on the body. Parameters ========== vec: Vector Defines the force vector. Can be any vector w.r.t any frame or combinations of frames. point: Point, optional Defines the point on which the force is applied. Default is the Body's center of mass. Example ======= The first example applies a gravitational force in the x direction of Body's frame to the body's center of mass. :: >>> from sympy import Symbol >>> from sympy.physics.mechanics import Body >>> body = Body('body') >>> g = Symbol('g') >>> body.apply_force(body.mass * g * body.frame.x) To apply force to any other point than center of mass, pass that point as well. This example applies a gravitational force to a point a distance l from the body's center of mass in the y direction. The force is again applied in the x direction. :: >>> from sympy import Symbol >>> from sympy.physics.mechanics import Body >>> body = Body('body') >>> g = Symbol('g') >>> l = Symbol('l') >>> point = body.masscenter.locatenew('force_point', l * ... body.frame.y) >>> body.apply_force(body.mass * g * body.frame.x, point) s+A Point must be supplied to apply force to.s)A Vector must be supplied to apply force.N(t isinstanceRRRt TypeErrorRRtappend(Rtvectpoint((s;lib/python2.7/site-packages/sympy/physics/mechanics/body.pyt apply_force‡s*  cCs;t|tƒstdƒ‚n|jj|j|fƒdS(s Adds a torque to the body. Parameters ========== vec: Vector Defines the torque vector. Can be any vector w.r.t any frame or combinations of frame. Example ======= This example adds a simple torque around the body's z axis. :: >>> from sympy import Symbol >>> from sympy.physics.mechanics import Body >>> body = Body('body') >>> T = Symbol('T') >>> body.apply_torque(T * body.frame.z) s(A Vector must be supplied to add torque.N(R"RR#RR$R(RR%((s;lib/python2.7/site-packages/sympy/physics/mechanics/body.pyt apply_torque»sN(t__name__t __module__t__doc__RRR'R((((s;lib/python2.7/site-packages/sympy/physics/mechanics/body.pyR s T  ' 4N( tsympy.core.backendRtsympy.physics.mechanicsRRRRtsympy.physics.vectorRRt__all__R(((s;lib/python2.7/site-packages/sympy/physics/mechanics/body.pyts"