o GZh(@sjddlmZmZmZmZmZmZddlmZddl m Z ddl m Z ddl mZdgZGddde ZdS) )Body Lagrangian KanesMethodLagrangesMethod RigidBodyParticle)BodyBase)_Methods)Matrix)sympy_deprecation_warning JointsMethodc@seZdZdZddZeddZeddZedd Zed d Z ed d Z eddZ eddZ eddZ eddZeddZddZddZddZddZd d!Zd"d#Zefd$d%Zd)d'd(Zd&S)*r a Method for formulating the equations of motion using a set of interconnected bodies with joints. .. deprecated:: 1.13 The JointsMethod class is deprecated. Its functionality has been replaced by the new :class:`~.System` class. 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 ======== As Body and JointsMethod have been deprecated, the following examples are for illustrative purposes only. The functionality of Body is fully captured by :class:`~.RigidBody` and :class:`~.Particle` and the functionality of JointsMethod is fully captured by :class:`~.System`. To ignore the deprecation warning we can use the ignore_warnings context manager. >>> from sympy.utilities.exceptions import ignore_warnings 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') >>> with ignore_warnings(DeprecationWarning): ... 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) >>> with ignore_warnings(DeprecationWarning): ... 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. cGsjtddddt|tr|j|_n||_||_||_||_| |_ | |_ | |_d|_dS)Nz The JointsMethod class is deprecated. Its functionality has been replaced by the new System class. z1.13z!deprecated-mechanics-jointsmethod)Zdeprecated_since_versionZactive_deprecations_target)r isinstancerframe_joints_generate_bodylist_bodies_generate_loadlist_loads _generate_q_q _generate_u_u_generate_kdes_kdes_method)selfZ newtonionZjointsrS/var/www/auris/lib/python3.10/site-packages/sympy/physics/mechanics/jointsmethod.py__init__^s        zJointsMethod.__init__cC|jS)zList of bodies in they system.)rrrrrbodiesuzJointsMethod.bodiescCr)zList of loads on the system.)rr rrrloadszr"zJointsMethod.loadscCrz$List of the generalized coordinates.)rr rrrqr"zJointsMethod.qcCr)zList of the generalized speeds.)rr rrrur"zJointsMethod.ucCrr$)rr rrrkdesr"zJointsMethod.kdescC|jjS)z)The "forcing vector" for the u's and q's.)method forcing_fullr rrrr*zJointsMethod.forcing_fullcCr()z&The "mass matrix" for the u's and q's.)r)mass_matrix_fullr rrrr,r+zJointsMethod.mass_matrix_fullcCr()zThe system's mass matrix.)r) mass_matrixr rrrr-r+zJointsMethod.mass_matrixcCr()zThe system's forcing vector.)r)forcingr rrrr.r+zJointsMethod.forcingcCr)z3Object of method used to form equations of systems.)rr rrrr)r"zJointsMethod.methodcCs@g}|jD]}|j|vr||j|j|vr||jq|SN)rchildappendparent)rr!jointrrrrs     zJointsMethod._generate_bodylistcCs*g}|jD] }t|tr||jq|Sr/)r!r rextendr#)r load_listbodyrrrrs    zJointsMethod._generate_loadlistcC>g}|jD]}|jD]}||vrtd||q qt|S)Nz'Coordinates of joints should be unique.)rZ coordinates ValueErrorr1r )rq_indr3Z coordinaterrrr   zJointsMethod._generate_qcCr7)Nz"Speeds of joints should be unique.)rZspeedsr8r1r )ru_indr3speedrrrrr:zJointsMethod._generate_ucCs*tddgj}|jD]}||j}q |S)Nr)r TrZcol_joinr')rZkd_indr3rrrrs zJointsMethod._generate_kdescCsg}|jD]<}t|ts||q|jr/t|j|j|j|j |j |jf}|j |_ ||qt |j|j|j }|j |_ ||q|Sr/) r!r rr1Z is_rigidbodyrnameZ masscenterrZmassZcentral_inertiaZpotential_energyr)rbodylistr6rbpartrrr_convert_bodiess      zJointsMethod._convert_bodiescCsl|}t|trt|jg|R}|||j|j||j|_n||j|j|j|j |j|d|_|j }|S)aMethod to form system's equation of motions. Parameters ========== method : Class Class name of method. Returns ======== Matrix Vector of equations of motions. Examples ======== As Body and JointsMethod have been deprecated, the following examples are for illustrative purposes only. The functionality of Body is fully captured by :class:`~.RigidBody` and :class:`~.Particle` and the functionality of JointsMethod is fully captured by :class:`~.System`. To ignore the deprecation warning we can use the ignore_warnings context manager. >>> from sympy.utilities.exceptions import ignore_warnings 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') >>> with ignore_warnings(DeprecationWarning): ... 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) >>> with ignore_warnings(DeprecationWarning): ... 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]]) )r9r;Zkd_eqsZ forcelistr!) rC issubclassrrrr%r#rr&r'r)Z _form_eoms)rr)r@LZsolnrrr form_eomss8  zJointsMethod.form_eomsNcCs|jj|dS)azReturns 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.matrixbase.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)r)rhs)rrGrrrrH#szJointsMethod.rhsr/)__name__ __module__ __qualname____doc__rpropertyr!r#r%r&r'r*r,r-r.r)rrrrrrCrrFrHrrrrr s>R              BN)Zsympy.physics.mechanicsrrrrrrZ!sympy.physics.mechanics.body_baserZsympy.physics.mechanics.methodr Zsympyr Zsympy.utilities.exceptionsr __all__r rrrrs