o 8Va @sFddlmZmZmZmZmZmZddlmZdgZ GdddeZ dS))Body Lagrangian KanesMethodLagrangesMethod RigidBodyParticle)_Methods 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 newtonionZjointsrF/usr/lib/python3/dist-packages/sympy/physics/mechanics/jointsmethod.py__init__Ms        zJointsMethod.__init__cC|jS)zList of bodies in they system.)rrrrrbodies\zJointsMethod.bodiescCr)zList of loads on the system.)rrrrrloadsar zJointsMethod.loadscCrz$List of the generalized coordinates.)rrrrrqfr zJointsMethod.qcCr)zList of the generalized speeds.)rrrrrukr zJointsMethod.ucCrr")rrrrrkdespr zJointsMethod.kdescC|jjS)z)The "forcing vector" for the u's and q's.)method forcing_fullrrrrr(uzJointsMethod.forcing_fullcCr&)z&The "mass matrix" for the u's and q's.)r'mass_matrix_fullrrrrr*zr)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 )r childappendparent)rrjointrrrrs     zJointsMethod._generate_bodylistcC g}|jD]}||jq|Sr )rextendr!)rZ load_listbodyrrrr zJointsMethod._generate_loadlistcC:g}|jD]}|jD]}||vrtd||q q|S)Nz'Coordinates of joints should be unique.)r Z coordinates ValueErrorr.)rq_indr0Z coordinaterrrr   zJointsMethod._generate_qcCr5)Nz"Speeds of joints should be unique.)r Zspeedsr6r.)ru_indr0Zspeedrrrrr8zJointsMethod._generate_ucCr1r )r r2r%)rZkd_indr0rrrrr4zJointsMethod._generate_kdescCsrg}|jD]1}|jr$t|j|j|j|j|j|jf}|j|_| |qt |j|j|j}|j|_| |q|Sr ) rZ is_rigidbodyrnameZ masscenterr ZmassZcentral_inertiaZpotential_energyr.r)rbodylistr3rbpartrrr_convert_bodiess    zJointsMethod._convert_bodiescCsl|}t|trt|jg|R}|||j|j||j|_n||j|j|j|j |j|d|_|j }|S)a7Method to form system's equation of motions. Parameters ========== method : Class Class name of method. Returns ======== Matrix Vector of equations of motions. Examples ======== This is a simple example for a one degree of freedom translational spring-mass-damper. >>> from sympy import S, symbols >>> from sympy.physics.mechanics import LagrangesMethod, dynamicsymbols, Body >>> from sympy.physics.mechanics import PrismaticJoint, JointsMethod >>> q = dynamicsymbols('q') >>> qd = dynamicsymbols('q', 1) >>> m, k, b = symbols('m k b') >>> wall = Body('W') >>> part = Body('P', mass=m) >>> part.potential_energy = k * q**2 / S(2) >>> J = PrismaticJoint('J', wall, part, coordinates=q, speeds=qd) >>> wall.apply_force(b * qd * wall.x, reaction_body=part) >>> method = JointsMethod(wall, J) >>> method.form_eoms(LagrangesMethod) Matrix([[b*Derivative(q(t), t) + k*q(t) + m*Derivative(q(t), (t, 2))]]) We can also solve for the states using the 'rhs' method. >>> method.rhs() Matrix([ [ Derivative(q(t), t)], [(-b*Derivative(q(t), t) - k*q(t))/m]]) )r7r9Zkd_eqsZ forcelistr) r> issubclassrrr r#r!rr$r%r'Z _form_eoms)rr'r;LZsolnrrr form_eomss-  zJointsMethod.form_eomsNcCs|jj|dS)aoReturns 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.KanesMethod.rhs(): KanesMethod's rhs function. sympy.physics.mechanics.LagrangesMethod.rhs(): LagrangesMethod's rhs function. ) inv_method)r'rhs)rrBrrrrCszJointsMethod.rhsr )__name__ __module__ __qualname____doc__rpropertyrr!r#r$r%r(r*r+r,r'rrrrrr>rrArCrrrrr s>D              7N) Zsympy.physics.mechanicsrrrrrrZsympy.physics.mechanics.methodr__all__r rrrrs