o eR!@sRddlmZmZmZmZmZmZddlmZddl m Z dgZ GdddeZ dS))Body Lagrangian KanesMethodLagrangesMethod RigidBodyParticle)_Methods)Matrix 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. 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. cGs\t|tr |j|_n||_||_||_||_||_ | |_ | |_ d|_dSN) isinstancerframe_joints_generate_bodylist_bodies_generate_loadlist_loads _generate_q_q _generate_u_u_generate_kdes_kdes_method)selfZ newtonionZjointsrTD:\Projects\ConvertPro\env\Lib\site-packages\sympy/physics/mechanics/jointsmethod.py__init__Ns        zJointsMethod.__init__cC|jS)zList of bodies in they system.)rrrrrbodies]zJointsMethod.bodiescCr)zList of loads on the system.)rrrrrloadsbr!zJointsMethod.loadscCrz$List of the generalized coordinates.)rrrrrqgr!zJointsMethod.qcCr)zList of the generalized speeds.)rrrrrulr!zJointsMethod.ucCrr#)rrrrrkdesqr!zJointsMethod.kdescC|jjS)z)The "forcing vector" for the u's and q's.)method forcing_fullrrrrr)vzJointsMethod.forcing_fullcCr')z&The "mass matrix" for the u's and q's.)r(mass_matrix_fullrrrrr+{r*zJointsMethod.mass_matrix_fullcCr')zThe system's mass matrix.)r( mass_matrixrrrrr,r*zJointsMethod.mass_matrixcCr')zThe system's forcing vector.)r(forcingrrrrr-r*zJointsMethod.forcingcCr)z3Object of method used to form equations of systems.)rrrrrr(r!zJointsMethod.methodcCs@g}|jD]}|j|vr||j|j|vr||jq|Sr )rchildappendparent)rr jointrrrrs     zJointsMethod._generate_bodylistcCs g}|jD]}||jq|Sr )r extendr")r load_listbodyrrrrs zJointsMethod._generate_loadlistcC>g}|jD]}|jD]}||vrtd||q qt|S)Nz'Coordinates of joints should be unique.)rZ coordinates ValueErrorr/r )rq_indr1Z coordinaterrrr   zJointsMethod._generate_qcCr5)Nz"Speeds of joints should be unique.)rZspeedsr6r/r )ru_indr1speedrrrrr8zJointsMethod._generate_ucCs*tddgj}|jD]}||j}q |S)Nr)r TrZcol_joinr&)rZkd_indr1rrrrs zJointsMethod._generate_kdescCsrg}|jD]1}|jr$t|j|j|j|j|j|jf}|j|_| |qt |j|j|j}|j|_| |q|Sr ) r Z is_rigidbodyrnameZ masscenterr ZmassZcentral_inertiaZpotential_energyr/r)rbodylistr4rbpartrrr_convert_bodiess    zJointsMethod._convert_bodiescCsl|}t|trt|jg|R}|||j|j||j|_n||j|j|j|j |j|d|_|j }|S)a7Method to form system's equation of motions. Parameters ========== method : Class Class name of method. Returns ======== Matrix Vector of equations of motions. Examples ======== This is a simple example for a one degree of freedom translational spring-mass-damper. >>> from sympy import S, symbols >>> from sympy.physics.mechanics import LagrangesMethod, dynamicsymbols, Body >>> from sympy.physics.mechanics import PrismaticJoint, JointsMethod >>> q = dynamicsymbols('q') >>> qd = dynamicsymbols('q', 1) >>> m, k, b = symbols('m k b') >>> wall = Body('W') >>> part = Body('P', mass=m) >>> part.potential_energy = k * q**2 / S(2) >>> J = PrismaticJoint('J', wall, part, coordinates=q, speeds=qd) >>> wall.apply_force(b * qd * wall.x, reaction_body=part) >>> method = JointsMethod(wall, J) >>> method.form_eoms(LagrangesMethod) Matrix([[b*Derivative(q(t), t) + k*q(t) + m*Derivative(q(t), (t, 2))]]) We can also solve for the states using the 'rhs' method. >>> method.rhs() Matrix([ [ Derivative(q(t), t)], [(-b*Derivative(q(t), t) - k*q(t))/m]]) )r7r9Zkd_eqsZ forcelistr ) rA issubclassrrr r$r"rr%r&r(Z _form_eoms)rr(r>LZsolnrrr form_eomss-  zJointsMethod.form_eomsNcCs|jj|dS)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)r(rhs)rrErrrrFszJointsMethod.rhsr )__name__ __module__ __qualname____doc__rpropertyr r"r$r%r&r)r+r,r-r(rrrrrrArrDrFrrrrr s>D              7N) Zsympy.physics.mechanicsrrrrrrZsympy.physics.mechanics.methodrZsympy.core.backendr __all__r rrrrs