+ i(r^RIHtHtHtHtHtHt^RIHt^RI H t ^RI H t ^RI HtR.t!RR] 4tR#) )Body Lagrangian KanesMethodLagrangesMethod RigidBodyParticle)BodyBase)_Methods)Matrix)sympy_deprecation_warning JointsMethodca]tRt^ toRtRt]R4t]R4t]R4t ]R4t ]R4t ]R4t ]R 4t ]R 4t]R 4t]R 4tR tRtRtRtRtRt]3RltRRltRtVtR#)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 Its functionality has been replaced by the new :class:`~.System` class.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. cj\RRRR7\V\4'dVPVnMWnW nVP 4VnVP4VnVP4Vn VP4Vn VP4VnRVnR#)z The JointsMethod class is deprecated. Its functionality has been replaced by the new System class. z1.13z!deprecated-mechanics-jointsmethod)deprecated_since_versionactive_deprecations_targetN)r isinstancer frame_joints_generate_bodylist_bodies_generate_loadlist_loads _generate_q_q _generate_u_u_generate_kdes_kdes_method)self newtonionjointss&&*ڄ/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/physics/mechanics/jointsmethod.py__init__JointsMethod.__init__^s! &,'J   i * *"DJ"J ..0 --/ ""$""$((*  c VP#)zList of bodies in they system.)rr s&r#bodiesJointsMethod.bodiesu||r&c VP#)zList of loads on the system.)rr(s&r#loadsJointsMethod.loadszs{{r&c VP#z$List of the generalized coordinates.)rr(s&r#qJointsMethod.q wwr&c VP#)zList of the generalized speeds.)rr(s&r#uJointsMethod.ur3r&c VP#r0)rr(s&r#kdesJointsMethod.kdesszzr&c .VPP#)z)The "forcing vector" for the u's and q's.)method forcing_fullr(s&r#r<JointsMethod.forcing_fulls{{'''r&c .VPP#)z&The "mass matrix" for the u's and q's.)r;mass_matrix_fullr(s&r#r?JointsMethod.mass_matrix_fulls{{+++r&c .VPP#)zThe system's mass matrix.)r; mass_matrixr(s&r#rBJointsMethod.mass_matrixs{{&&&r&c .VPP#)zThe system's forcing vector.)r;forcingr(s&r#rEJointsMethod.forcings{{"""r&c VP#)z3Object of method used to form equations of systems.)rr(s&r#r;JointsMethod.methodr+r&c.pVPF]pVPV9dVPVP4VPV9gKBVPVP4K_ V#N)rchildappendparent)r r)joints& r#rJointsMethod._generate_bodylistsT\\E{{&( ekk*||6) ell+ "  r&c.pVPF6p\V\4'gKVPVP4K8 V#rJ)r)rrextendr-)r load_listbodys& r#rJointsMethod._generate_loadlists< KKD$%%  , r&c.pVPF8pVPF%pW19d \R4hVPV4K' K: \ V4#)z'Coordinates of joints should be unique.)r coordinates ValueErrorrLr )r q_indrN coordinates& r#rJointsMethod._generate_qsO\\E#// &$%NOO Z(0" e}r&c.pVPF8pVPF%pW19d \R4hVPV4K' K: \ V4#)z"Speeds of joints should be unique.)rspeedsrWrLr )r u_indrNspeeds& r#rJointsMethod._generate_usL\\E>$%IJJ U#&" e}r&c\^^.4PpVPFpVPVP4pK V#))r Trcol_joinr8)r kd_indrNs& r#rJointsMethod._generate_kdess;1b!##\\E__UZZ0F" r&c ".pVPFp\V\4'gVPV4K,VP'dr\ VP VPVPVPVPVP34pVPVn VPV4K\VP VPVP4pVPVn VPV4K V#rJ) r)rrrL is_rigidbodyrname masscenterrmasscentral_inertiapotential_energyr)r bodylistrSrbparts& r#_convert_bodiesJointsMethod._convert_bodiessKKDdD))%   tyy$//4::tyy))4??;=&*&;&;## 4??DIIF(,(=(=%% r&c  VP4p\V\4'dF\VP.VO5!pV!W0P VP W P4VnMEV!VPVP VPVPVP VR7VnVPP4pV#)aBMethod to form system's equation of motions. Parameters ========== method : Class Class name of method. Returns ======== Matrix Vector of equations of motions. Examples ======== As Body and JointsMethod have been deprecated, the following examples are for illustrative purposes only. The functionality of Body is fully captured by :class:`~.RigidBody` and :class:`~.Particle` and the functionality of JointsMethod is fully captured by :class:`~.System`. To ignore the deprecation warning we can use the ignore_warnings context manager. >>> from sympy.utilities.exceptions import ignore_warnings This is a simple example for a one degree of freedom translational spring-mass-damper. >>> from sympy import S, symbols >>> from sympy.physics.mechanics import LagrangesMethod, dynamicsymbols, Body >>> from sympy.physics.mechanics import PrismaticJoint, JointsMethod >>> q = dynamicsymbols('q') >>> qd = dynamicsymbols('q', 1) >>> m, k, b = symbols('m k b') >>> with ignore_warnings(DeprecationWarning): ... wall = Body('W') ... part = Body('P', mass=m) >>> part.potential_energy = k * q**2 / S(2) >>> J = PrismaticJoint('J', wall, part, coordinates=q, speeds=qd) >>> wall.apply_force(b * qd * wall.x, reaction_body=part) >>> with ignore_warnings(DeprecationWarning): ... method = JointsMethod(wall, J) >>> method.form_eoms(LagrangesMethod) Matrix([[b*Derivative(q(t), t) + k*q(t) + m*Derivative(q(t), (t, 2))]]) We can also solve for the states using the 'rhs' method. >>> method.rhs() Matrix([ [ Derivative(q(t), t)], [(-b*Derivative(q(t), t) - k*q(t))/m]]) )rXr]kd_eqs forcelistr)) rp issubclassrrrr1r-rr5r8r; _form_eoms)r r;rmLsolns&& r# form_eomsJointsMethod.form_eomssp'') fo . .4::11A!!VVTZZ::NDL!$**DFF$&&QUQZQZ.2jjKDL{{%%' r&Nc :VPPVR7#)aReturns equations that can be solved numerically. Parameters ========== inv_method : str The specific sympy inverse matrix calculation method to use. For a list of valid methods, see :meth:`~sympy.matrices.matrixbase.MatrixBase.inv` Returns ======== Matrix Numerically solvable equations. See Also ======== sympy.physics.mechanics.kane.KanesMethod.rhs: KanesMethod's rhs function. sympy.physics.mechanics.lagrange.LagrangesMethod.rhs: LagrangesMethod's rhs function. ) inv_method)r;rhs)r r|s&&r#r}JointsMethod.rhs#s6{{*55r&)rrrrrrrrrJ)__name__ __module__ __qualname____firstlineno____doc__r$propertyr)r-r1r5r8r<r?rBrEr;rrrrrrprryr}__static_attributes____classdictcell__) __classdict__s@r#r r s Pd.((,,''## $ +@D66r&N)sympy.physics.mechanicsrrrrrr!sympy.physics.mechanics.body_baser sympy.physics.mechanics.methodr sympyr sympy.utilities.exceptionsr __all__r r&r#rs19963@  s68s6r&