\h(pSSKJrJrJrJrJrJr SSKJr SSK J r SSK J r SSK Jr S/r"SS\ 5rg) )Body Lagrangian KanesMethodLagrangesMethod RigidBodyParticle)BodyBase)_Methods)Matrix)sympy_deprecation_warning JointsMethodc\rSrSrSrSr\S5r\S5r\S5r \S5r \S5r \S 5r \S 5r \S 5r\S 5r\S 5rSrSrSrSrSrSr\4SjrSSjrSrg)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 Its functionality has been replaced by the new :class:`~.System` class.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. c`[SSSS9 [U[5(aURUlOXlX lUR 5UlUR5UlUR5Ul UR5Ul UR5UlSUlg)Nz The JointsMethod class is deprecated. Its functionality has been replaced by the new System class. z1.13z!deprecated-mechanics-jointsmethod)deprecated_since_versionactive_deprecations_target)r isinstancer frame_joints_generate_bodylist_bodies_generate_loadlist_loads _generate_q_q _generate_u_u_generate_kdes_kdes_method)self newtonionjointss \/var/www/auris/envauris/lib/python3.13/site-packages/sympy/physics/mechanics/jointsmethod.py__init__JointsMethod.__init__^s! &,'J   i * *"DJ"J ..0 --/ ""$""$((*  cUR$)zList of bodies in they system.)rr!s r$bodiesJointsMethod.bodiesu||r'cUR$)zList of loads on the system.)rr)s r$loadsJointsMethod.loadszs{{r'cUR$z$List of the generalized coordinates.)rr)s r$qJointsMethod.q wwr'cUR$)zList of the generalized speeds.)rr)s r$uJointsMethod.ur4r'cUR$r1)rr)s r$kdesJointsMethod.kdesszzr'c.URR$)z)The "forcing vector" for the u's and q's.)method forcing_fullr)s r$r=JointsMethod.forcing_fulls{{'''r'c.URR$)z&The "mass matrix" for the u's and q's.)r<mass_matrix_fullr)s r$r@JointsMethod.mass_matrix_fulls{{+++r'c.URR$)zThe system's mass matrix.)r< mass_matrixr)s r$rCJointsMethod.mass_matrixs{{&&&r'c.URR$)zThe system's forcing vector.)r<forcingr)s r$rFJointsMethod.forcings{{"""r'cUR$)z3Object of method used to form equations of systems.)r r)s r$r<JointsMethod.methodr,r'c/nURH[nURU;aURUR5 URU;dM@URUR5 M] U$N)rchildappendparent)r!r*joints r$rJointsMethod._generate_bodylistsT\\E{{&( ekk*||6) ell+ "  r'c/nURH5n[U[5(dMURUR5 M7 U$rK)r*rrextendr.)r! load_listbodys r$rJointsMethod._generate_loadlists< KKD$%%  , r'c/nURH7nURH$nX1;a [S5eURU5 M& M9 [ U5$)Nz'Coordinates of joints should be unique.)r coordinates ValueErrorrMr )r!q_indrO coordinates r$rJointsMethod._generate_qsO\\E#// &$%NOO Z(0" e}r'c/nURH7nURH$nX1;a [S5eURU5 M& M9 [ U5$)Nz"Speeds of joints should be unique.)rspeedsrXrMr )r!u_indrOspeeds r$rJointsMethod._generate_usL\\E>$%IJJ U#&" e}r'c[SS/5RnURHnURUR5nM U$)Nr)r Trcol_joinr9)r!kd_indrOs r$rJointsMethod._generate_kdess;1b!##\\E__UZZ0F" r'c /nURHn[U[5(dURU5 M+UR(aq[ UR URURURURUR45nURUl URU5 M[UR URUR5nURUl URU5 M U$rK) r*rrrM is_rigidbodyrname masscenterrmasscentral_inertiapotential_energyr)r!bodylistrTrbparts r$_convert_bodiesJointsMethod._convert_bodiessKKDdD))%  tyy$//4::tyy))4??;=&*&;&;## 4??DIIF(,(=(=%% r'c UR5n[U[5(aD[UR/UQ76nU"X0R UR X R5UlOBU"URUR URURUR US9UlURR5nU$)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]]) )rYr^kd_eqs forcelistr*) rq issubclassrrrr2r.r r6r9r< _form_eoms)r!r<rnLsolns r$ form_eomsJointsMethod.form_eomssp'') fo . .4::11A!!VVTZZ::NDL!$**DFF$&&QUQZQZ.2jjKDL{{%%' r'Nc4URRUS9$)aReturns equations that can be solved numerically. Parameters ========== inv_method : str The specific sympy inverse matrix calculation method to use. For a list of valid methods, see :meth:`~sympy.matrices.matrixbase.MatrixBase.inv` Returns ======== Matrix Numerically solvable equations. See Also ======== sympy.physics.mechanics.kane.KanesMethod.rhs: KanesMethod's rhs function. sympy.physics.mechanics.lagrange.LagrangesMethod.rhs: LagrangesMethod's rhs function. ) inv_method)r<rhs)r!r}s r$r~JointsMethod.rhs#s6{{*55r')rrrrr rrrrK)__name__ __module__ __qualname____firstlineno____doc__r%propertyr*r.r2r6r9r=r@rCrFr<rrrrrrqrrzr~__static_attributes__r'r$r r sPd.((,,''## $ +@D6r'N)sympy.physics.mechanicsrrrrrr!sympy.physics.mechanics.body_baser sympy.physics.mechanics.methodr sympyr sympy.utilities.exceptionsr __all__r rr'r$rs19963@  s68s6r'