Initialisation du repository de Beta

venv/lib/python3.12/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/chaos_pendulum.al

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+CONSTANTS G,LB,W,H
+MOTIONVARIABLES' THETA'',PHI'',OMEGA',ALPHA'
+NEWTONIAN N
+BODIES A,B
+SIMPROT(N,A,2,THETA)
+SIMPROT(A,B,3,PHI)
+POINT O
+LA = (LB-H/2)/2
+P_O_AO> = LA*A3>
+P_O_BO> = LB*A3>
+OMEGA = THETA'
+ALPHA = PHI'
+W_A_N> = OMEGA*N2>
+W_B_A> = ALPHA*A3>
+V_O_N> = 0>
+V2PTS(N, A, O, AO)
+V2PTS(N, A, O, BO)
+MASS A=MA, B=MB
+IAXX = 1/12*MA*(2*LA)^2
+IAYY = IAXX
+IAZZ = 0
+IBXX = 1/12*MB*H^2
+IBYY = 1/12*MB*(W^2+H^2)
+IBZZ = 1/12*MB*W^2
+INERTIA A, IAXX, IAYY, IAZZ
+INERTIA B, IBXX, IBYY, IBZZ
+GRAVITY(G*N3>)
+ZERO = FR() + FRSTAR()
+KANE()
+INPUT LB=0.2,H=0.1,W=0.2,MA=0.01,MB=0.1,G=9.81
+INPUT THETA = 90 DEG, PHI = 0.5 DEG, OMEGA=0, ALPHA=0
+INPUT TFINAL=10, INTEGSTP=0.02
+CODE DYNAMICS() some_filename.c

venv/lib/python3.12/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/chaos_pendulum.py

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+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+g, lb, w, h = _sm.symbols('g lb w h', real=True)
+theta, phi, omega, alpha = _me.dynamicsymbols('theta phi omega alpha')
+theta_d, phi_d, omega_d, alpha_d = _me.dynamicsymbols('theta_ phi_ omega_ alpha_', 1)
+theta_dd, phi_dd = _me.dynamicsymbols('theta_ phi_', 2)
+frame_n = _me.ReferenceFrame('n')
+body_a_cm = _me.Point('a_cm')
+body_a_cm.set_vel(frame_n, 0)
+body_a_f = _me.ReferenceFrame('a_f')
+body_a = _me.RigidBody('a', body_a_cm, body_a_f, _sm.symbols('m'), (_me.outer(body_a_f.x,body_a_f.x),body_a_cm))
+body_b_cm = _me.Point('b_cm')
+body_b_cm.set_vel(frame_n, 0)
+body_b_f = _me.ReferenceFrame('b_f')
+body_b = _me.RigidBody('b', body_b_cm, body_b_f, _sm.symbols('m'), (_me.outer(body_b_f.x,body_b_f.x),body_b_cm))
+body_a_f.orient(frame_n, 'Axis', [theta, frame_n.y])
+body_b_f.orient(body_a_f, 'Axis', [phi, body_a_f.z])
+point_o = _me.Point('o')
+la = (lb-h/2)/2
+body_a_cm.set_pos(point_o, la*body_a_f.z)
+body_b_cm.set_pos(point_o, lb*body_a_f.z)
+body_a_f.set_ang_vel(frame_n, omega*frame_n.y)
+body_b_f.set_ang_vel(body_a_f, alpha*body_a_f.z)
+point_o.set_vel(frame_n, 0)
+body_a_cm.v2pt_theory(point_o,frame_n,body_a_f)
+body_b_cm.v2pt_theory(point_o,frame_n,body_a_f)
+ma = _sm.symbols('ma')
+body_a.mass = ma
+mb = _sm.symbols('mb')
+body_b.mass = mb
+iaxx = 1/12*ma*(2*la)**2
+iayy = iaxx
+iazz = 0
+ibxx = 1/12*mb*h**2
+ibyy = 1/12*mb*(w**2+h**2)
+ibzz = 1/12*mb*w**2
+body_a.inertia = (_me.inertia(body_a_f, iaxx, iayy, iazz, 0, 0, 0), body_a_cm)
+body_b.inertia = (_me.inertia(body_b_f, ibxx, ibyy, ibzz, 0, 0, 0), body_b_cm)
+force_a = body_a.mass*(g*frame_n.z)
+force_b = body_b.mass*(g*frame_n.z)
+kd_eqs = [theta_d - omega, phi_d - alpha]
+forceList = [(body_a.masscenter,body_a.mass*(g*frame_n.z)), (body_b.masscenter,body_b.mass*(g*frame_n.z))]
+kane = _me.KanesMethod(frame_n, q_ind=[theta,phi], u_ind=[omega, alpha], kd_eqs = kd_eqs)
+fr, frstar = kane.kanes_equations([body_a, body_b], forceList)
+zero = fr+frstar
+from pydy.system import System
+sys = System(kane, constants = {g:9.81, lb:0.2, w:0.2, h:0.1, ma:0.01, mb:0.1},
+specifieds={},
+initial_conditions={theta:_np.deg2rad(90), phi:_np.deg2rad(0.5), omega:0, alpha:0},
+times = _np.linspace(0.0, 10, 10/0.02))
+
+y=sys.integrate()

venv/lib/python3.12/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/double_pendulum.al

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+MOTIONVARIABLES' Q{2}', U{2}'
+CONSTANTS L,M,G
+NEWTONIAN N
+FRAMES A,B
+SIMPROT(N, A, 3, Q1)
+SIMPROT(N, B, 3, Q2)
+W_A_N>=U1*N3>
+W_B_N>=U2*N3>
+POINT O
+PARTICLES P,R
+P_O_P> = L*A1>
+P_P_R> = L*B1>
+V_O_N> = 0>
+V2PTS(N, A, O, P)
+V2PTS(N, B, P, R)
+MASS P=M, R=M
+Q1' = U1
+Q2' = U2
+GRAVITY(G*N1>)
+ZERO = FR() + FRSTAR()
+KANE()
+INPUT M=1,G=9.81,L=1
+INPUT Q1=.1,Q2=.2,U1=0,U2=0
+INPUT TFINAL=10, INTEGSTP=.01
+CODE DYNAMICS() some_filename.c

venv/lib/python3.12/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/double_pendulum.py

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+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+q1, q2, u1, u2 = _me.dynamicsymbols('q1 q2 u1 u2')
+q1_d, q2_d, u1_d, u2_d = _me.dynamicsymbols('q1_ q2_ u1_ u2_', 1)
+l, m, g = _sm.symbols('l m g', real=True)
+frame_n = _me.ReferenceFrame('n')
+frame_a = _me.ReferenceFrame('a')
+frame_b = _me.ReferenceFrame('b')
+frame_a.orient(frame_n, 'Axis', [q1, frame_n.z])
+frame_b.orient(frame_n, 'Axis', [q2, frame_n.z])
+frame_a.set_ang_vel(frame_n, u1*frame_n.z)
+frame_b.set_ang_vel(frame_n, u2*frame_n.z)
+point_o = _me.Point('o')
+particle_p = _me.Particle('p', _me.Point('p_pt'), _sm.Symbol('m'))
+particle_r = _me.Particle('r', _me.Point('r_pt'), _sm.Symbol('m'))
+particle_p.point.set_pos(point_o, l*frame_a.x)
+particle_r.point.set_pos(particle_p.point, l*frame_b.x)
+point_o.set_vel(frame_n, 0)
+particle_p.point.v2pt_theory(point_o,frame_n,frame_a)
+particle_r.point.v2pt_theory(particle_p.point,frame_n,frame_b)
+particle_p.mass = m
+particle_r.mass = m
+force_p = particle_p.mass*(g*frame_n.x)
+force_r = particle_r.mass*(g*frame_n.x)
+kd_eqs = [q1_d - u1, q2_d - u2]
+forceList = [(particle_p.point,particle_p.mass*(g*frame_n.x)), (particle_r.point,particle_r.mass*(g*frame_n.x))]
+kane = _me.KanesMethod(frame_n, q_ind=[q1,q2], u_ind=[u1, u2], kd_eqs = kd_eqs)
+fr, frstar = kane.kanes_equations([particle_p, particle_r], forceList)
+zero = fr+frstar
+from pydy.system import System
+sys = System(kane, constants = {l:1, m:1, g:9.81},
+specifieds={},
+initial_conditions={q1:.1, q2:.2, u1:0, u2:0},
+times = _np.linspace(0.0, 10, 10/.01))
+
+y=sys.integrate()

venv/lib/python3.12/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/mass_spring_damper.al

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+CONSTANTS M,K,B,G
+MOTIONVARIABLES' POSITION',SPEED'
+VARIABLES O
+FORCE = O*SIN(T)
+NEWTONIAN CEILING
+POINTS ORIGIN
+V_ORIGIN_CEILING> = 0>
+PARTICLES BLOCK
+P_ORIGIN_BLOCK> = POSITION*CEILING1>
+MASS BLOCK=M
+V_BLOCK_CEILING>=SPEED*CEILING1>
+POSITION' = SPEED
+FORCE_MAGNITUDE = M*G-K*POSITION-B*SPEED+FORCE
+FORCE_BLOCK>=EXPLICIT(FORCE_MAGNITUDE*CEILING1>)
+ZERO = FR() + FRSTAR()
+KANE()
+INPUT TFINAL=10.0, INTEGSTP=0.01
+INPUT M=1.0, K=1.0, B=0.2, G=9.8, POSITION=0.1, SPEED=-1.0, O=2
+CODE DYNAMICS() dummy_file.c

venv/lib/python3.12/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/mass_spring_damper.py

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+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+m, k, b, g = _sm.symbols('m k b g', real=True)
+position, speed = _me.dynamicsymbols('position speed')
+position_d, speed_d = _me.dynamicsymbols('position_ speed_', 1)
+o = _me.dynamicsymbols('o')
+force = o*_sm.sin(_me.dynamicsymbols._t)
+frame_ceiling = _me.ReferenceFrame('ceiling')
+point_origin = _me.Point('origin')
+point_origin.set_vel(frame_ceiling, 0)
+particle_block = _me.Particle('block', _me.Point('block_pt'), _sm.Symbol('m'))
+particle_block.point.set_pos(point_origin, position*frame_ceiling.x)
+particle_block.mass = m
+particle_block.point.set_vel(frame_ceiling, speed*frame_ceiling.x)
+force_magnitude = m*g-k*position-b*speed+force
+force_block = (force_magnitude*frame_ceiling.x).subs({position_d:speed})
+kd_eqs = [position_d - speed]
+forceList = [(particle_block.point,(force_magnitude*frame_ceiling.x).subs({position_d:speed}))]
+kane = _me.KanesMethod(frame_ceiling, q_ind=[position], u_ind=[speed], kd_eqs = kd_eqs)
+fr, frstar = kane.kanes_equations([particle_block], forceList)
+zero = fr+frstar
+from pydy.system import System
+sys = System(kane, constants = {m:1.0, k:1.0, b:0.2, g:9.8},
+specifieds={_me.dynamicsymbols('t'):lambda x, t: t, o:2},
+initial_conditions={position:0.1, speed:-1*1.0},
+times = _np.linspace(0.0, 10.0, 10.0/0.01))
+
+y=sys.integrate()

venv/lib/python3.12/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/non_min_pendulum.al

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+MOTIONVARIABLES' Q{2}''
+CONSTANTS L,M,G
+NEWTONIAN N
+POINT PN
+V_PN_N> = 0>
+THETA1 = ATAN(Q2/Q1)
+FRAMES A
+SIMPROT(N, A, 3, THETA1)
+PARTICLES P
+P_PN_P> = Q1*N1>+Q2*N2>
+MASS P=M
+V_P_N>=DT(P_P_PN>, N)
+F_V = DOT(EXPRESS(V_P_N>,A), A1>)
+GRAVITY(G*N1>)
+DEPENDENT[1] = F_V
+CONSTRAIN(DEPENDENT[Q1'])
+ZERO=FR()+FRSTAR()
+F_C = MAG(P_P_PN>)-L
+CONFIG[1]=F_C
+ZERO[2]=CONFIG[1]

venv/lib/python3.12/site-packages/sympy/parsing/autolev/test-examples/pydy-example-repo/non_min_pendulum.py

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+import sympy.physics.mechanics as _me
+import sympy as _sm
+import math as m
+import numpy as _np
+
+q1, q2 = _me.dynamicsymbols('q1 q2')
+q1_d, q2_d = _me.dynamicsymbols('q1_ q2_', 1)
+q1_dd, q2_dd = _me.dynamicsymbols('q1_ q2_', 2)
+l, m, g = _sm.symbols('l m g', real=True)
+frame_n = _me.ReferenceFrame('n')
+point_pn = _me.Point('pn')
+point_pn.set_vel(frame_n, 0)
+theta1 = _sm.atan(q2/q1)
+frame_a = _me.ReferenceFrame('a')
+frame_a.orient(frame_n, 'Axis', [theta1, frame_n.z])
+particle_p = _me.Particle('p', _me.Point('p_pt'), _sm.Symbol('m'))
+particle_p.point.set_pos(point_pn, q1*frame_n.x+q2*frame_n.y)
+particle_p.mass = m
+particle_p.point.set_vel(frame_n, (point_pn.pos_from(particle_p.point)).dt(frame_n))
+f_v = _me.dot((particle_p.point.vel(frame_n)).express(frame_a), frame_a.x)
+force_p = particle_p.mass*(g*frame_n.x)
+dependent = _sm.Matrix([[0]])
+dependent[0] = f_v
+velocity_constraints = [i for i in dependent]
+u_q1_d = _me.dynamicsymbols('u_q1_d')
+u_q2_d = _me.dynamicsymbols('u_q2_d')
+kd_eqs = [q1_d-u_q1_d, q2_d-u_q2_d]
+forceList = [(particle_p.point,particle_p.mass*(g*frame_n.x))]
+kane = _me.KanesMethod(frame_n, q_ind=[q1,q2], u_ind=[u_q2_d], u_dependent=[u_q1_d], kd_eqs = kd_eqs, velocity_constraints = velocity_constraints)
+fr, frstar = kane.kanes_equations([particle_p], forceList)
+zero = fr+frstar
+f_c = point_pn.pos_from(particle_p.point).magnitude()-l
+config = _sm.Matrix([[0]])
+config[0] = f_c
+zero = zero.row_insert(zero.shape[0], _sm.Matrix([[0]]))
+zero[zero.shape[0]-1] = config[0]