Ed!TddlmZmZmZmZmZmZddlmZdgZ GddeZ dS))Body Lagrangian KanesMethodLagrangesMethod RigidBodyParticle)_Methods 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__Ms i & & #"DJJ"DJ ..00 --// ""$$""$$((**  c|jS)zList of bodies in they system.)rrs rbodieszJointsMethod.bodies\ |r!c|jS)zList of loads on the system.)rr#s rloadszJointsMethod.loadsas {r!c|jSz$List of the generalized coordinates.)rr#s rqzJointsMethod.qf wr!c|jS)zList of the generalized speeds.)rr#s ruzJointsMethod.ukr+r!c|jSr))rr#s rkdeszJointsMethod.kdesps zr!c|jjS)z)The "forcing vector" for the u's and q's.)method forcing_fullr#s rr2zJointsMethod.forcing_fullus{''r!c|jjS)z&The "mass matrix" for the u's and q's.)r1mass_matrix_fullr#s rr4zJointsMethod.mass_matrix_fullzs{++r!c|jjS)zThe system's mass matrix.)r1 mass_matrixr#s rr6zJointsMethod.mass_matrixs{&&r!c|jjS)zThe system's forcing vector.)r1forcingr#s rr8zJointsMethod.forcings{""r!c|jS)z3Object of method used to form equations of systems.)rr#s rr1zJointsMethod.methodr%r!cg}|jD]H}|j|vr||j|j|vr||jI|Sr )rchildappendparent)rr$joints rrzJointsMethod._generate_bodylistsd\ , ,E{&( + ek***|6) , el+++ r!cRg}|jD]}||j|Sr )r$extendr')r load_listbodys rrzJointsMethod._generate_loadlists7 K ) )D   TZ ( ( ( (r!cg}|jD]4}|jD]*}||vrtd||+5|S)Nz'Coordinates of joints should be unique.)r coordinates ValueErrorr<)rq_indr> coordinates rrzJointsMethod._generate_qsh\ ) )E#/ ) ) &P$%NOOO Z(((( ) r!cg}|jD]4}|jD]*}||vrtd||+5|S)Nz"Speeds of joints should be unique.)rspeedsrEr<)ru_indr>speeds rrzJointsMethod._generate_usf\ $ $E $ $E>K$%IJJJ U#### $ r!cRg}|jD]}||j|Sr )rr@r/)rkd_indr>s rrzJointsMethod._generate_kdess4\ & &E MM%* % % % % 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)rbodylistrBrbparts r_convert_bodieszJointsMethod._convert_bodiessK & &D  &ty$/4:ty)4?;==&*&;##### 4?DIFF(,(=%%%%%r!cT|}t|tr6t|jg|R}|||j|j||j|_n/||j|j|j|j |j||_|j }|S)a7Method to form system's equation of motions. Parameters ========== method : Class Class name of method. Returns ======== Matrix Vector of equations of motions. Examples ======== This is a simple example for a one degree of freedom translational spring-mass-damper. >>> from sympy import S, symbols >>> from sympy.physics.mechanics import LagrangesMethod, dynamicsymbols, Body >>> from sympy.physics.mechanics import PrismaticJoint, JointsMethod >>> q = dynamicsymbols('q') >>> qd = dynamicsymbols('q', 1) >>> m, k, b = symbols('m k b') >>> wall = Body('W') >>> part = Body('P', mass=m) >>> part.potential_energy = k * q**2 / S(2) >>> J = PrismaticJoint('J', wall, part, coordinates=q, speeds=qd) >>> wall.apply_force(b * qd * wall.x, reaction_body=part) >>> method = JointsMethod(wall, J) >>> method.form_eoms(LagrangesMethod) Matrix([[b*Derivative(q(t), t) + k*q(t) + m*Derivative(q(t), (t, 2))]]) We can also solve for the states using the 'rhs' method. >>> method.rhs() Matrix([ [ Derivative(q(t), t)], [(-b*Derivative(q(t), t) - k*q(t))/m]]) )rFrJkd_eqs forcelistr$) rX issubclassrrrr*r'rr-r/r1 _form_eoms)rr1rULsolns r form_eomszJointsMethod.form_eomssZ'')) fo . . K4:1111A!6!TVTZ4:NNDLL!6$*DF$&QUQZ.2jKKKDL{%%'' r!Nc8|j|S)a}Returns 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 solveable 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)r1rhs)rrbs rrczJointsMethod.rhss6{*555r!r )__name__ __module__ __qualname____doc__r propertyr$r'r*r-r/r2r4r6r8r1rrrrrrXrr`rcr!rr r sBBH   XXXXX((X(,,X,''X'##X#X     +5555n666666r!N) sympy.physics.mechanicsrrrrrrsympy.physics.mechanics.methodr __all__r rir!rrms9999999999999999333333  N6N6N6N6N68N6N6N6N6N6r!