Ed*RddlmZddlmZmZmZddlmZdgZGddZ dS))sympify)PointReferenceFrameDyadic)sympy_deprecation_warning RigidBodycfeZdZdZdZdZdZedZej dZedZ e j dZ ed Z e j d Z ed Z e j d Z ed Z dZdZdZedZej dZdZdZdS)raAn idealized rigid body. Explanation =========== This is essentially a container which holds the various components which describe a rigid body: a name, mass, center of mass, reference frame, and inertia. All of these need to be supplied on creation, but can be changed afterwards. Attributes ========== name : string The body's name. masscenter : Point The point which represents the center of mass of the rigid body. frame : ReferenceFrame The ReferenceFrame which the rigid body is fixed in. mass : Sympifyable The body's mass. inertia : (Dyadic, Point) The body's inertia about a point; stored in a tuple as shown above. Examples ======== >>> from sympy import Symbol >>> from sympy.physics.mechanics import ReferenceFrame, Point, RigidBody >>> from sympy.physics.mechanics import outer >>> m = Symbol('m') >>> A = ReferenceFrame('A') >>> P = Point('P') >>> I = outer (A.x, A.x) >>> inertia_tuple = (I, P) >>> B = RigidBody('B', P, A, m, inertia_tuple) >>> # Or you could change them afterwards >>> m2 = Symbol('m2') >>> B.mass = m2 ct|tstd||_||_||_||_||_d|_dS)NzSupply a valid name.r) isinstancestr TypeError_name masscentermassframeinertiapotential_energy)selfnamerrrrs Alib/python3.11/site-packages/sympy/physics/mechanics/rigidbody.py__init__zRigidBody.__init__7sT$$$ 4233 3 $   !c|jSN)rrs r__str__zRigidBody.__str__As zrc*|Sr)rrs r__repr__zRigidBody.__repr__Ds||~~rc|jSr)_framers rrzRigidBody.frameGs {rc\t|tstd||_dS)Nz/RigdBody frame must be a ReferenceFrame object.)r rr r )rFs rrzRigidBody.frameKs/!^,, OMNN N rc|jSr) _masscenterrs rrzRigidBody.masscenterQs rc\t|tstd||_dS)Nz0RigidBody center of mass must be a Point object.)r rr r$)rps rrzRigidBody.masscenterUs2!U## PNOO Orc|jSr)_massrs rrzRigidBody.mass[s zrc.t||_dSr)rr()rms rrzRigidBody.mass_sQZZ rc|j|jfSr)_inertia_inertia_pointrs rrzRigidBody.inertiacs t233rcxt|dtstdt|dtstd|d|_|d|_ddlm}||j|j |d|j }|d|z |_ dS)Nrz*RigidBody inertia must be a Dyadic object.z(RigidBody inertia must be about a Point.)inertia_of_point_mass) r rr rr,r-!sympy.physics.mechanics.functionsr0rrpos_fromr_central_inertia)rIr0I_Ss_Os rrzRigidBody.inertiags!A$'' JHII I!A$&& HFGG G! d LKKKKK&&ty'+'?'?!'E'E'+z33!"!v rc|jS)z"The body's central inertia dyadic.)r3rs rcentral_inertiazRigidBody.central_inertiaxs $$rcF|j|j|zS)a Linear momentum of the rigid body. Explanation =========== The linear momentum L, of a rigid body B, with respect to frame N is given by L = M * v* where M is the mass of the rigid body and v* is the velocity of the mass center of B in the frame, N. Parameters ========== frame : ReferenceFrame The frame in which linear momentum is desired. Examples ======== >>> from sympy.physics.mechanics import Point, ReferenceFrame, outer >>> from sympy.physics.mechanics import RigidBody, dynamicsymbols >>> from sympy.physics.vector import init_vprinting >>> init_vprinting(pretty_print=False) >>> M, v = dynamicsymbols('M v') >>> N = ReferenceFrame('N') >>> P = Point('P') >>> P.set_vel(N, v * N.x) >>> I = outer (N.x, N.x) >>> Inertia_tuple = (I, P) >>> B = RigidBody('B', P, N, M, Inertia_tuple) >>> B.linear_momentum(N) M*v*N.x )rrvel)rrs rlinear_momentumzRigidBody.linear_momentum}s"Ny4?..u5555rc|j}|j|}|j}|j|}|j|}|||||zzS)a|Returns the angular momentum of the rigid body about a point in the given frame. Explanation =========== The angular momentum H of a rigid body B about some point O in a frame N is given by: H = I . w + r x Mv where I is the central inertia dyadic of B, w is the angular velocity of body B in the frame, N, r is the position vector from point O to the mass center of B, and v is the velocity of the mass center in the frame, N. Parameters ========== point : Point The point about which angular momentum is desired. frame : ReferenceFrame The frame in which angular momentum is desired. Examples ======== >>> from sympy.physics.mechanics import Point, ReferenceFrame, outer >>> from sympy.physics.mechanics import RigidBody, dynamicsymbols >>> from sympy.physics.vector import init_vprinting >>> init_vprinting(pretty_print=False) >>> M, v, r, omega = dynamicsymbols('M v r omega') >>> N = ReferenceFrame('N') >>> b = ReferenceFrame('b') >>> b.set_ang_vel(N, omega * b.x) >>> P = Point('P') >>> P.set_vel(N, 1 * N.x) >>> I = outer(b.x, b.x) >>> B = RigidBody('B', P, b, M, (I, P)) >>> B.angular_momentum(P, N) omega*b.x ) r7r ang_vel_inrrr2r9dotcross)rpointrr4wr*rvs rangular_momentumzRigidBody.angular_momentumsvX   J ! !% ( ( I O $ $U + + O   & &uuQxx!''!a%..((rc@|j||j|j|ztdz z}|j|j||j|zztdz }||zS)a>Kinetic energy of the rigid body. Explanation =========== The kinetic energy, T, of a rigid body, B, is given by 'T = 1/2 (I omega^2 + m v^2)' where I and m are the central inertia dyadic and mass of rigid body B, respectively, omega is the body's angular velocity and v is the velocity of the body's mass center in the supplied ReferenceFrame. Parameters ========== frame : ReferenceFrame The RigidBody's angular velocity and the velocity of it's mass center are typically defined with respect to an inertial frame but any relevant frame in which the velocities are known can be supplied. Examples ======== >>> from sympy.physics.mechanics import Point, ReferenceFrame, outer >>> from sympy.physics.mechanics import RigidBody >>> from sympy import symbols >>> M, v, r, omega = symbols('M v r omega') >>> N = ReferenceFrame('N') >>> b = ReferenceFrame('b') >>> b.set_ang_vel(N, omega * b.x) >>> P = Point('P') >>> P.set_vel(N, v * N.x) >>> I = outer (b.x, b.x) >>> inertia_tuple = (I, P) >>> B = RigidBody('B', P, b, M, inertia_tuple) >>> B.kinetic_energy(N) M*v**2/2 + omega**2/2 )rr<r7rrrr9)rr rotational_KEtranslational_KEs rkinetic_energyzRigidBody.kinetic_energysT..u559M %%e,,:-07 9;; !I)<)>> from sympy.physics.mechanics import RigidBody, Point, outer, ReferenceFrame >>> from sympy import symbols >>> M, g, h = symbols('M g h') >>> b = ReferenceFrame('b') >>> P = Point('P') >>> I = outer (b.x, b.x) >>> Inertia_tuple = (I, P) >>> B = RigidBody('B', P, b, M, Inertia_tuple) >>> B.potential_energy = M * g * h >>> B.potential_energy M*g*h )_pers rrzRigidBody.potential_energy s *xrc.t||_dS)aUsed to set the potential energy of this RigidBody. Parameters ========== scalar: Sympifyable The potential energy (a scalar) of the RigidBody. Examples ======== >>> from sympy.physics.mechanics import Point, outer >>> from sympy.physics.mechanics import RigidBody, ReferenceFrame >>> from sympy import symbols >>> b = ReferenceFrame('b') >>> M, g, h = symbols('M g h') >>> P = Point('P') >>> I = outer (b.x, b.x) >>> Inertia_tuple = (I, P) >>> B = RigidBody('B', P, b, M, Inertia_tuple) >>> B.potential_energy = M * g * h N)rrJrscalars rrzRigidBody.potential_energy#s46??rc8tddd||_dS)Nz The sympy.physics.mechanics.RigidBody.set_potential_energy() method is deprecated. Instead use B.potential_energy = scalar z1.5zdeprecated-set-potential-energy)deprecated_since_versionactive_deprecations_target)rrrLs rset_potential_energyzRigidBody.set_potential_energy?s6!  "'#D !'rc ddlm}|j||j\}}}|j||j|dz|dzz|dz|dzz|dz|dzz| |z| |z| |zz}|j|zS)aReturns the inertia dyadic of the body with respect to another point. Parameters ========== point : sympy.physics.vector.Point The point to express the inertia dyadic about. Returns ======= inertia : sympy.physics.vector.Dyadic The inertia dyadic of the rigid body expressed about the provided point. r)rrE)r1rrr2 to_matrixrrr7)rr?rabcr4s r parallel_axiszRigidBody.parallel_axisNs& >=====/**511;;DJGG1a I AqD1a4KA1ad !1G%'(b1fqb1fqb1f>> >#a''rN)__name__ __module__ __qualname____doc__rrrpropertyrsetterrrrr7r:rCrHrrQrWrrrr s**X"""X \\   X  X [  [ 44X4 ^..^. %%X%'6'6'6R2)2)2)h000000dX,###6 ' ' '(((((rN) sympy.core.backendrsympy.physics.vectorrrrsympy.utilities.exceptionsr__all__rr^rrrcs&&&&&&>>>>>>>>>>@@@@@@ -[([([([([([([([([([(r