def plot_eval():
#### Eigenvalue plot #####
u2 = arange(-30, 30.01, 0.01, dtype=complex)
n = len(u1)
eval = zeros((n,3), dtype=complex)
for i, u in enumerate(u1):
eval[i] = rd.evals(u, (g, r))
mnmx = array([min([min(eval[:,1].imag), min(eval[:,1].real)]),
max([max(eval[:,0].real), max(eval[:,0].imag)])])
cs = rd.critical_speed((g,r))
cs = array([cs, cs])
plt.figure()
plt.plot(u2, eval[:,0].real, 'r', label='Re($\lambda_0$)')
plt.plot(u2, eval[:,1].real, 'b', label='Re($\lambda_1$)')
plt.plot(u2, eval[:,0].imag, 'r:', label='Im($\lambda_0$)')
plt.plot(u2, eval[:,1].imag, 'b:', label='Im($\lambda_1$)')
plt.plot(cs, mnmx, 'g:', linewidth=2)
plt.plot(-cs, mnmx, 'g:', linewidth=2)
plt.title('Eigenvalues of linearized EOMS about upright steady configuration,\n'+
'm=%.4f kg, r=%.4f m'%(m,r))
plt.xlabel('$u_2$ [rad / s] Spin rate')
plt.axis('tight')
plt.grid()
plt.legend(loc=0)
plt.show()
def plot_eval():
#### Eigenvalue plot #####
u2 = arange(-30, 30.01, 0.01, dtype=complex)
n = len(u1)
eval = zeros((n, 3), dtype=complex)
for i, u in enumerate(u1):
eval[i] = rd.evals(u, (g, r))
mnmx = array([
min([min(eval[:, 1].imag), min(eval[:, 1].real)]),
max([max(eval[:, 0].real), max(eval[:, 0].imag)])
])
cs = rd.critical_speed((g, r))
cs = array([cs, cs])
plt.figure()
plt.plot(u2, eval[:, 0].real, 'r', label='Re($\lambda_0$)')
plt.plot(u2, eval[:, 1].real, 'b', label='Re($\lambda_1$)')
plt.plot(u2, eval[:, 0].imag, 'r:', label='Im($\lambda_0$)')
plt.plot(u2, eval[:, 1].imag, 'b:', label='Im($\lambda_1$)')
plt.plot(cs, mnmx, 'g:', linewidth=2)
plt.plot(-cs, mnmx, 'g:', linewidth=2)
plt.title(
'Eigenvalues of linearized EOMS about upright steady configuration,\n'
+ 'm=%.4f kg, r=%.4f m' % (m, r))
plt.xlabel('$u_2$ [rad / s] Spin rate')
plt.axis('tight')
plt.grid()
plt.legend(loc=0)
plt.show()
# Eigenvalue plot #plot_eval() # states = [q1, q2, q3, q4, q5, u1, u2, u3] # q1, q2, q3 are Body Fixed (Euler) 3-1-2 angles # q1: Yaw / heading angle # q2: Lean angle # q3: Spin angle # q4, q5 are N[1], N[2] Inertial positions of contact point # u1, u2, u3 are the body fixed components of angular velocity # Gravity is in the positive N[3] direction (into the ground) # Specify the initial conditions of the coordinates lean = 0.1 qi = [pi/4, lean, 0.0, .001, 0.001] cs = rd.critical_speed((g,r)) # Initial condition above critical speed: ui = [.1, cs[0]*2.1, 0.0] ui = [.1, cs[0], 0.0] # Initial condition below critical speed: ui = [.1, cs[0]*.6, 0.0] animate_steady = False xi = set_ics(qi, ui, animate_steady) # Integration time ti = 0.0 ts = 0.001 tf = 1.0 t = arange(ti, tf+ts, ts) n = len(t) # Integrate the differential equations
# Eigenvalue plot #plot_eval() # states = [q1, q2, q3, q4, q5, u1, u2, u3] # q1, q2, q3 are Body Fixed (Euler) 3-1-2 angles # q1: Yaw / heading angle # q2: Lean angle # q3: Spin angle # q4, q5 are N[1], N[2] Inertial positions of contact point # u1, u2, u3 are the body fixed components of angular velocity # Gravity is in the positive N[3] direction (into the ground) # Specify the initial conditions of the coordinates lean = 0.1 qi = [pi / 4, lean, 0.0, .001, 0.001] cs = rd.critical_speed((g, r)) # Initial condition above critical speed: ui = [.1, cs[0] * 2.1, 0.0] ui = [.1, cs[0], 0.0] # Initial condition below critical speed: ui = [.1, cs[0] * .6, 0.0] animate_steady = False xi = set_ics(qi, ui, animate_steady) # Integration time ti = 0.0 ts = 0.001 tf = 1.0 t = arange(ti, tf + ts, ts) n = len(t) # Integrate the differential equations
