RieR!`ddlmZmZmZmZmZmZddlmZddl m Z dgZ GddeZ dS))Body Lagrangian KanesMethodLagrangesMethod RigidBodyParticle)_Methods)Matrix JointsMethodc*eZdZdZdZedZedZedZedZ edZ edZ ed Z ed Z ed Zed Zd ZdZdZdZdZdZefdZddZdS)r a%Method for formulating the equations of motion using a set of interconnected bodies with joints. Parameters ========== newtonion : Body or ReferenceFrame The newtonion(inertial) frame. *joints : Joint The joints in the system Attributes ========== q, u : iterable Iterable of the generalized coordinates and speeds bodies : iterable Iterable of Body objects in the system. loads : iterable Iterable of (Point, vector) or (ReferenceFrame, vector) tuples describing the forces on the system. mass_matrix : Matrix, shape(n, n) The system's mass matrix forcing : Matrix, shape(n, 1) The system's forcing vector mass_matrix_full : Matrix, shape(2*n, 2*n) The "mass matrix" for the u's and q's forcing_full : Matrix, shape(2*n, 1) The "forcing vector" for the u's and q's method : KanesMethod or Lagrange's method Method's object. kdes : iterable Iterable of kde in they system. Examples ======== This is a simple example for a one degree of freedom translational spring-mass-damper. >>> from sympy import symbols >>> from sympy.physics.mechanics import Body, JointsMethod, PrismaticJoint >>> from sympy.physics.vector import dynamicsymbols >>> c, k = symbols('c k') >>> x, v = dynamicsymbols('x v') >>> wall = Body('W') >>> body = Body('B') >>> J = PrismaticJoint('J', wall, body, coordinates=x, speeds=v) >>> wall.apply_force(c*v*wall.x, reaction_body=body) >>> wall.apply_force(k*x*wall.x, reaction_body=body) >>> method = JointsMethod(wall, J) >>> method.form_eoms() Matrix([[-B_mass*Derivative(v(t), t) - c*v(t) - k*x(t)]]) >>> M = method.mass_matrix_full >>> F = method.forcing_full >>> rhs = M.LUsolve(F) >>> rhs Matrix([ [ v(t)], [(-c*v(t) - k*x(t))/B_mass]]) Notes ===== ``JointsMethod`` currently only works with systems that do not have any configuration or motion constraints. cnt|tr |j|_n||_||_||_||_||_ | |_ | |_ d|_dSN) isinstancerframe_joints_generate_bodylist_bodies_generate_loadlist_loads _generate_q_q _generate_u_u_generate_kdes_kdes_method)self newtonionjointss Dlib/python3.11/site-packages/sympy/physics/mechanics/jointsmethod.py__init__zJointsMethod.__init__Ns i & & #"DJJ"DJ ..00 --// ""$$""$$((**  c|jS)zList of bodies in they system.)rrs r bodieszJointsMethod.bodies] |r"c|jS)zList of loads on the system.)rr$s r loadszJointsMethod.loadsbs {r"c|jSz$List of the generalized coordinates.)rr$s r qzJointsMethod.qg wr"c|jS)zList of the generalized speeds.)rr$s r uzJointsMethod.ulr,r"c|jSr*)rr$s r kdeszJointsMethod.kdesqs zr"c|jjS)z)The "forcing vector" for the u's and q's.)method forcing_fullr$s r r3zJointsMethod.forcing_fullvs{''r"c|jjS)z&The "mass matrix" for the u's and q's.)r2mass_matrix_fullr$s r r5zJointsMethod.mass_matrix_full{s{++r"c|jjS)zThe system's mass matrix.)r2 mass_matrixr$s r r7zJointsMethod.mass_matrixs{&&r"c|jjS)zThe system's forcing vector.)r2forcingr$s r r9zJointsMethod.forcings{""r"c|jS)z3Object of method used to form equations of systems.)rr$s r r2zJointsMethod.methodr&r"cg}|jD]H}|j|vr||j|j|vr||jI|Sr)rchildappendparent)rr%joints r rzJointsMethod._generate_bodylists`\ , ,E{&(( ek***|6)) el+++ r"cRg}|jD]}||j|Sr)r%extendr()r load_listbodys r rzJointsMethod._generate_loadlists7 K ) )D   TZ ( ( ( (r"cg}|jD]4}|jD]*}||vrtd||+5t |S)Nz'Coordinates of joints should be unique.)r coordinates ValueErrorr=r )rq_indr? coordinates r rzJointsMethod._generate_qsl\ ) )E#/ ) ) &&$%NOOO Z(((( )e}}r"cg}|jD]4}|jD]*}||vrtd||+5t |S)Nz"Speeds of joints should be unique.)rspeedsrFr=r )ru_indr?speeds r rzJointsMethod._generate_usi\ $ $E $ $E>>$%IJJJ U#### $e}}r"cztddgj}|jD]}||j}|S)Nr)r Trcol_joinr0)rkd_indr?s r rzJointsMethod._generate_kdessA1b!!#\ 1 1E__UZ00FF r"c Xg}|jD]}|jrUt|j|j|j|j|j|jf}|j|_| |^t|j|j|j}|j|_| ||Sr) r% is_rigidbodyrname masscenterrmasscentral_inertiapotential_energyr=r)rbodylistrCrbparts r _convert_bodieszJointsMethod._convert_bodiessK & &D  &ty$/4:ty)4?;==&*&;##### 4?DIFF(,(=%%%%%r"cT|}t|tr6t|jg|R}|||j|j||j|_n/||j|j|j|j |j||_|j }|S)a7Method to form system's equation of motions. Parameters ========== method : Class Class name of method. Returns ======== Matrix Vector of equations of motions. Examples ======== This is a simple example for a one degree of freedom translational spring-mass-damper. >>> from sympy import S, symbols >>> from sympy.physics.mechanics import LagrangesMethod, dynamicsymbols, Body >>> from sympy.physics.mechanics import PrismaticJoint, JointsMethod >>> q = dynamicsymbols('q') >>> qd = dynamicsymbols('q', 1) >>> m, k, b = symbols('m k b') >>> wall = Body('W') >>> part = Body('P', mass=m) >>> part.potential_energy = k * q**2 / S(2) >>> J = PrismaticJoint('J', wall, part, coordinates=q, speeds=qd) >>> wall.apply_force(b * qd * wall.x, reaction_body=part) >>> method = JointsMethod(wall, J) >>> method.form_eoms(LagrangesMethod) Matrix([[b*Derivative(q(t), t) + k*q(t) + m*Derivative(q(t), (t, 2))]]) We can also solve for the states using the 'rhs' method. >>> method.rhs() Matrix([ [ Derivative(q(t), t)], [(-b*Derivative(q(t), t) - k*q(t))/m]]) )rGrKkd_eqs forcelistr%) r\ issubclassrrrr+r(rr.r0r2 _form_eoms)rr2rYLsolns r form_eomszJointsMethod.form_eomssZ'')) fo . . K4:1111A!6!TVTZ4:NNDLL!6$*DF$&QUQZ.2jKKKDL{%%'' r"Nc8|j|S)axReturns equations that can be solved numerically. Parameters ========== inv_method : str The specific sympy inverse matrix calculation method to use. For a list of valid methods, see :meth:`~sympy.matrices.matrices.MatrixBase.inv` Returns ======== Matrix Numerically solvable equations. See Also ======== sympy.physics.mechanics.kane.KanesMethod.rhs: KanesMethod's rhs function. sympy.physics.mechanics.lagrange.LagrangesMethod.rhs: LagrangesMethod's rhs function. ) inv_method)r2rhs)rrfs r rgzJointsMethod.rhss6{*555r"r)__name__ __module__ __qualname____doc__r!propertyr%r(r+r.r0r3r5r7r9r2rrrrrr\rrdrgr"r r r sBBH   XXXXX((X(,,X,''X'##X#X     +5555n666666r"N) sympy.physics.mechanicsrrrrrrsympy.physics.mechanics.methodr sympy.core.backendr __all__r rmr"r rrs9999999999999999333333%%%%%%  N6N6N6N6N68N6N6N6N6N6r"