def eig(self, speeds):
'''Returns the eigenvalues and eigenvectors of the Whipple bicycle
model linearized about the nominal configuration.
Parameters
----------
speeds : ndarray, shape (n,) or float
The speed at which to calculate the eigenvalues.
Returns
-------
evals : ndarray, shape (n, 4)
eigenvalues
evecs : ndarray, shape (n, 4, 4)
eigenvectors
Notes
-----
If you have a flywheel defined, body D, it will completely be ignored
in these results. These results are strictly for the Whipple bicycle
model.
'''
# this allows you to enter a float
try:
speeds.shape
except AttributeError:
speeds = np.array([speeds])
par = io.remove_uncertainties(self.parameters['Benchmark'])
M, C1, K0, K2 = bicycle.benchmark_par_to_canonical(par)
m, n = 4, speeds.shape[0]
evals = np.zeros((n, m), dtype='complex128')
evecs = np.zeros((n, m, m), dtype='complex128')
for i, speed in enumerate(speeds):
A, B = bicycle.ab_matrix(M, C1, K0, K2, speed, par['g'])
w, v = np.linalg.eig(A)
evals[i] = w
evecs[i] = v
return evals, evecs
def eig(self, speeds):
'''Returns the eigenvalues and eigenvectors of the Whipple bicycle
model linearized about the nominal configuration.
Parameters
----------
speeds : ndarray, shape (n,) or float
The speed at which to calculate the eigenvalues.
Returns
-------
evals : ndarray, shape (n, 4)
eigenvalues
evecs : ndarray, shape (n, 4, 4)
eigenvectors
Notes
-----
If you have a flywheel defined, body D, it will completely be ignored
in these results. These results are strictly for the Whipple bicycle
model.
'''
# this allows you to enter a float
try:
speeds.shape
except AttributeError:
speeds = np.array([speeds])
par = io.remove_uncertainties(self.parameters['Benchmark'])
M, C1, K0, K2 = bicycle.benchmark_par_to_canonical(par)
m, n = 4, speeds.shape[0]
evals = np.zeros((n, m), dtype='complex128')
evecs = np.zeros((n, m, m), dtype='complex128')
for i, speed in enumerate(speeds):
A, B = bicycle.ab_matrix(M, C1, K0, K2, speed, par['g'])
w, v = np.linalg.eig(A)
evals[i] = w
evecs[i] = v
return evals, evecs
def canonical(self, nominal=False):
"""
Returns the canonical velocity and gravity independent matrices for
the Whipple bicycle model linearized about the nominal
configuration.
Parameters
----------
nominal : boolean, optional
The default is false and uarrays are returned with the
calculated uncertainties. If true ndarrays are returned without
uncertainties.
Returns
-------
M : uarray, shape(2,2)
Mass matrix.
C1 : uarray, shape(2,2)
Velocity independent damping matrix.
K0 : uarray, shape(2,2)
Gravity independent part of the stiffness matrix.
K2 : uarray, shape(2,2)
Velocity squared independent part of the stiffness matrix.
Notes
-----
The canonical matrices complete the following equation:
M * q'' + v * C1 * q' + [g * K0 + v**2 * K2] * q = f
where:
q = [phi, delta]
f = [Tphi, Tdelta]
phi
Bicycle roll angle.
delta
Steer angle.
Tphi
Roll torque.
Tdelta
Steer torque.
v
Bicylce speed.
If you have a flywheel defined, body D, it will completely be
ignored in these results. These results are strictly for the Whipple
bicycle model.
"""
par = self.parameters['Benchmark']
M, C1, K0, K2 = bicycle.benchmark_par_to_canonical(par)
if nominal is True:
return (unumpy.nominal_values(M), unumpy.nominal_values(C1),
unumpy.nominal_values(K0), unumpy.nominal_values(K2))
elif nominal is False:
return M, C1, K0, K2
else:
raise ValueError('nominal must be True or False')
def canonical(self, nominal=False):
"""
Returns the canonical velocity and gravity independent matrices for the
Whipple bicycle model linearized about the nominal configuration.
Returns
-------
M : uarray, shape(2,2)
Mass matrix.
C1 : uarray, shape(2,2)
Velocity independent damping matrix.
K0 : uarray, shape(2,2)
Gravity independent part of the stiffness matrix.
K2 : uarray, shape(2,2)
Velocity squared independent part of the stiffness matrix.
nominal : boolean, optional
The default is false and uarrays are returned with the calculated
uncertainties. If true ndarrays are returned without uncertainties.
Notes
-----
The canonical matrices complete the following equation:
M * q'' + v * C1 * q' + [g * K0 + v**2 * K2] * q = f
where:
q = [phi, delta]
f = [Tphi, Tdelta]
phi
Bicycle roll angle.
delta
Steer angle.
Tphi
Roll torque.
Tdelta
Steer torque.
v
Bicylce speed.
If you have a flywheel defined, body D, it will completely be ignored
in these results. These results are strictly for the Whipple bicycle
model.
"""
par = self.parameters['Benchmark']
M, C1, K0, K2 = bicycle.benchmark_par_to_canonical(par)
if nominal is True:
return (unumpy.nominal_values(M),
unumpy.nominal_values(C1),
unumpy.nominal_values(K0),
unumpy.nominal_values(K2))
elif nominal is False:
return M, C1, K0, K2
else:
raise ValueError('nominal must be True or False')
