variables = [qA, qB, qC]
guess = [initialvalues[item] for item in variables]
result = c.solve_numeric(variables, guess, system.constant_values)
guess = [initialvalues[item] for item in variables]
ini = []
for item in system.get_state_variables():
if item in variables:
ini.append(result.x[variables.index(item)])
else:
ini.append(initialvalues[item])
points = PointsOutput(points, constant_values=system.constant_values)
points.calc(numpy.array([ini0, ini]))
points.plot_time()
eq_d = sympy.Matrix(eq_d)
qi = sympy.Matrix([qA_d])
qd = sympy.Matrix([qB_d, qC_d])
C = eq_d.jacobian(qi)
D = eq_d.jacobian(qd)
J = -D.inv() * C
J.simplify()
qd2 = J * qi
subs = dict([(ii, jj) for ii, jj in zip(qd, qd2)])
# In[28]:
# KE = system.get_KE()
# PE = system.getPEGravity(pNA) - system.getPESprings()
# energy_output = Output([KE-PE],system)
# energy_output.calc(states)
# energy_output.plot_time()
# ### Motion
# In[29]:
points = [pm1, pNA, pAB, pBC, pC1, pC2]
points_output = PointsOutput(points, system)
y = points_output.calc(states)
points_output.plot_time(5)
# #### Motion Animation
# in normal Python the next lines of code produce an animation using matplotlib
# In[30]:
points_output.animate(fps=fps,
movie_name='render.mp4',
lw=2,
marker='o',
color=(1, 0, 0, 1),
linestyle='-')
#a()
# To plot the animation in jupyter you need a couple extra lines of code...
'constants': constants
}, ))
return states
input_data_all = run_sim([1.1e2, 9e2])
input_positions = input_data_all[:, :3]
# input_positions = input_positions.copy()
# pynamics.integration.logger.setLevel(logging.ERROR)
pynamics.system.logger.setLevel(logging.ERROR)
points = [pNA, pAB, pBC, pCtip]
points_output = PointsOutput(points, system)
y = points_output.calc(input_data_all)
points_output.plot_time()
r = numpy.random.randn(*(y.shape)) * .01
y_rand = y + r
fy = scipy.interpolate.interp1d(t, y_rand.transpose((1, 2, 0)))
fyt = fy(t)
# points_output.animate(fps = fps,movie_name = 'render.mp4',lw=2,marker='o',color=(1,0,0,1),linestyle='-')
def calc_error(args):
states_guess = run_sim(args)
y_guess = points_output.calc(states_guess).transpose((1, 2, 0))
error = fyt - y_guess
error **= 2
error = error.sum()
# # =============================================================================
# KE = system.get_KE()
# PE = system.getPEGravity(0*N.x) - system.getPESprings()
# energy = Output([KE-PE], constant_values = constants)
# energy.calc(states,t)
# energy.plot_time()
# # =============================================================================
# positions = Output(system.get_q(0), constant_values = constants)
# positions.calc(states,t)
# positions.plot_time()
# speeds = Output(system.get_q(1), constant_values = constants)
# speeds.calc(states,t)
# speeds.plot_time()
# y= Output([G*qB_d], constant_values=constants)
# y.calc(states,t)
# y.plot_time()
points = [pAcm, pBcm]
po = PointsOutput(points, constant_values=constants)
po.calc(states, t)
po.plot_time()
po.animate(fps=fps,
movie_name='triple_pendulum.mp4',
lw=2,
marker='o',
color=(1, 0, 0, 1),
linestyle='-')
ini,
t,
rtol=tol,
atol=tol,
args=({
'constants': constants
}, ))
points = [pm1, pm2]
po2 = PointsOutput(points, system, constant_values=system.constant_values)
po2.calc(states)
constants[b_constraint] = 0
states = pynamics.integration.integrate_odeint(func,
ini,
t,
rtol=tol,
atol=tol,
args=({
'constants': constants
}, ))
points = [pm1, pm2]
po3 = PointsOutput(points, system, constant_values=system.constant_values)
po3.calc(states)
po.plot_time()
po.animate(fps=fps, movie_name='bouncy-mod.mp4', lw=2, marker='o')
po2.plot_time()
po2.animate(fps=fps, movie_name='bouncy-mod.mp4', lw=2, marker='o')
po3.plot_time()
po3.animate(fps=fps, movie_name='bouncy-mod.mp4', lw=2, marker='o')
plt.legend(artists,['qA','qB','qC']) # Plot --- energy KE = system.get_KE() PE = system.getPEGravity(pNA) - system.getPESprings() energy_output = Output([KE-PE],system) energy_output.calc(states) energy_output.plot_time() # Motion points = [pNA,pAB,pBtip,pBC, pCD] points_output = PointsOutput(points,system) y = points_output.calc(states) points_output.plot_time(20) points_output.animate(fps = 30,lw=2) from matplotlib import animation, rc from IPython.display import HTML HTML(points_output.anim.to_html5_video()) """From the animation above, we see that because we set the neutral position of the device to stand straight (vertical sides for the four-bar mechanism), our device would not just freely drop to the ground. # 6. Tuning: Now adjust the damper value to something nonzero, that over 10s shows that the system is settling. """ b = Constant(1e0,'b',system) system.addforce(-b*wNA,wNA)
c=KinematicConstraint(eq)
variables = [qA,qB,qC,qD]
guess = [initialvalues[item] for item in variables]
result = c.solve_numeric(variables,guess,system.constant_values)
ini = []
for item in system.get_state_variables():
if item in variables:
ini.append(result[item])
else:
ini.append(initialvalues[item])
po1 = PointsOutput(points, constant_values=system.constant_values)
po1.calc(numpy.array([ini0,ini]),[0,1])
po1.plot_time()
# po1.calc(numpy.array([ini,ini]),[0,1])
# po1.plot_time()
pAcm = pNA+lA/2*A.x
pBcm = pAB+lA/2*B.x
pCcm = pNC+lA/2*C.x
pDcm = pCD+lA/2*D.x
vBD = pBD.time_derivative()
vDB = pDB.time_derivative()
wNA = N.get_w_to(A)
wAB = A.get_w_to(B)
