def test_annulus():
"""
Tests annulus function vs explicit annulus formula up to L=5. Full annulus.
"""
qcyl = qlm.annulus(5, 1, 1, 2, 3, 0, np.pi)
qcyl2 = qlmA.annulus(5, 1/(5*np.pi), 1, 2, 3, 0, np.pi)
assert (abs(qcyl-qcyl2) < 30*np.finfo(float).eps).all()
def test_cylinder2():
"""
Tests recursive cylinder function vs annulus formula up to L=10. That is
the annulus formula should be consistent with the recursive cylinder
calculation.
"""
qcyl = qlm.cylinder(10, 1, 1, 1)
qcyl2 = qlm.annulus(10, 1, 1, 0, 1, 0, np.pi)
assert (abs(qcyl-qcyl2) < 10*np.finfo(float).eps).all()
def __init__(self, N, lmax, inner, mass, H, Ri, Ro, phic, phih):
Shape.__init__(self, N, lmax, inner)
self.mass = mass
if self.inner:
self.qlm = qlm.annulus(lmax, mass, H, Ri, Ro, phic, phih)
else:
dens = mass/(2*phih*(Ro**2 - Ri**2)*H)
self.qlm = bqlm.annulus(lmax, dens, H/2, Ri, Ro, phic, phih)
self.qlm += bqlm.annulus(lmax, dens, -H/2, Ri, Ro, phic, phih)
self.pointmass = gshp.wedge(mass, Ri, Ro, H, phih, N, N)
self.pointmass = glb.rotate_point_array(self.pointmass, phic,
[0, 0, 1])
def test_annulus2():
"""
Tests annulus function vs explicit annulus formula up to L=5. Partial.
"""
qcyl = qlm.annulus(5, 1, 1, 2, 3, np.pi/3, np.pi/8)
rho = 8/(np.pi*(3**2-2**2))
qcyl2 = qlmA.annulus(5, rho, 1, 2, 3, np.pi/3, np.pi/8)
assert (abs(qcyl-qcyl2) < 90*np.finfo(float).eps).all()
qcyl3 = qlmN.cyl_mom(5, rho, np.pi/8, 2, 3, -.5, .5)
qcyl3 = rot.rotate_qlm(qcyl3, np.pi/3, 0, 0)
assert (abs(qcyl-qcyl2) < 90*np.finfo(float).eps).all()
# Test explicit formula for L<5 (we'll do L=3)
qcyl2 = qlmA.annulus(3, rho, 1, 2, 3, np.pi/3, np.pi/8)
assert (np.shape(qcyl2) == (4, 7))
def read_mpc(LMax, filename, filepath='C:\\mpc\\'):
"""
Attempts to open .mpc files in the same manner as MULTIN by having a
'working register' and a 'total register'. That is, there are two sets of
moments stored in memory. One is the sum of all the previous moments
(total) and the other is the current shape (working) being manipulated. The
working shape can be rotated, translated, and added to total sequentially
many times. This function does not allow the use of 'recall', 'store',
'rescale', or 'save' statements currently. Takes an optional filepath which
is assumed to be the standard filepath for MULTIN, 'C:\\mpc\\'.
Inputs
------
LMax : int
Highest degree inner multipole moments to compute
filename : str
Name of .mpc file (with or without extension)
filepath : str, optional
Directory containing .mpc file, assumed 'C:\\mpc\\' in MULTIN
Returns
-------
qlmTot : ndarray, complex
Complex (LMax+1)x(2LMax + 1) array of inner multipole coefficients
"""
if not filename.endswith('.mpc'):
filename += '.mpc'
with open(filepath + filename) as f:
lines = f.readlines()
title = lines[0]
print(title)
# We don't actually use n integration in this
nsteps = 25
# Assume units are centimeters unless told otherwise
fac = 1e-2
nlines = len(lines[1:])
qlmTot = np.zeros([LMax + 1, 2 * LMax + 1], dtype='complex')
qlmWrk = np.zeros([LMax + 1, 2 * LMax + 1], dtype='complex')
k = 0
while k < nlines:
line = lines[1 + k]
# Get rid of stuff after a comment
line = line.split('%')[0]
if 'create' in line:
print(line)
shape = line.split('create')[1].split()[0]
if shape == 'cylinder':
line2 = [float(val) for val in lines[2 + k].split(',')]
Ri, Ro, H, phi0, phi1 = line2
Ri, Ro, H = Ri * fac, Ro * fac, H * fac
phic = (phi1 + phi0) * np.pi / 180 / 2
phih = (phi1 - phi0) * np.pi / 180 / 2
dens = float(lines[3 + k].split(',')[0]) * 1000
mass = dens * phih * H * (Ro**2 - Ri**2)
print(dens, line2)
qlmWrk = qlm.annulus(LMax, mass, H, Ri, Ro, phic, phih)
pos = np.array(lines[4 + k].split(','), dtype=float) * fac
k += 3
if (pos == 0).all() and ('add' in lines[2 + k]):
k += 1
print('added ', shape)
qlmTot += qlmWrk
else:
print('translated ', shape)
qlmWrk = trs.translate_qlm(qlmWrk, pos)
elif shape == 'sphere':
line2 = [float(val) * fac for val in lines[2 + k].split(',')]
r = line2[0]
dens = float(lines[3 + k].split(',')[0]) * 1000
mass = dens * 4 / 3 * np.pi * r**3
qlmWrk = qlm.sphere(LMax, mass, r)
pos = np.array(lines[4 + k].split(','), dtype=float) * fac
k += 3
if (pos == 0).all() and ('add' in lines[2 + k]):
k += 1
print('added ', shape)
qlmTot += qlmWrk
else:
print('translated ', shape)
qlmWrk = trs.translate_qlm(qlmWrk, pos)
elif shape == 'cone':
line2 = [float(val) * fac for val in lines[2 + k].split(',')]
LR, UR, H = line2
dens = float(lines[3 + k].split(',')[0]) * 1000
mass = dens * np.pi * H * LR**2 / 3
print(LR, UR, H, dens, mass)
qlmWrk = qlm.cone(LMax, mass, H, LR, 0, np.pi)
pos = np.array(lines[4 + k].split(','), dtype=float) * fac
k += 3
if (pos == 0).all() and ('add' in lines[2 + k]):
k += 1
print('added ', shape)
qlmTot += qlmWrk
else:
print('translated ', shape)
qlmWrk = trs.translate_qlm(qlmWrk, pos)
elif shape == 'triangle':
line2 = [float(val) * fac for val in lines[2 + k].split(',')]
d, y1, y2, t = line2
dens = float(lines[3 + k].split(',')[0]) * 1000
mass = dens * t * d * abs(y2 - y1) / 2
qlmWrk = qlm.tri_prism(LMax, mass, t, d, y1, y2)
pos = np.array(lines[4 + k].split(','), dtype=float) * fac
k += 3
if (pos == 0).all() and ('add' in lines[2 + k]):
k += 1
print('added ', shape)
qlmTot += qlmWrk
else:
print('translated ', shape)
qlmWrk = trs.translate_qlm(qlmWrk, pos)
elif shape == 'trapezoid':
line2 = [float(val) * fac for val in lines[2 + k].split(',')]
w1, w2, h, t = line2
if w2 < w1:
w3, w4 = w2, w1
flip = True
else:
w3, w4 = w1, w2
flip = False
dens = float(lines[3 + k].split(',')[0]) * 1000
y1, y2 = w3 / 2, w4 / 2
hs = w3 * h / (w4 - w3)
hb = h + hs
massTrib = dens * t * w4 * hb / 2
massTris = dens * t * w3 * hs / 2
print(hs, hb, w3, w4)
qlmWrk = qlm.tri_iso_prism(LMax, massTrib, t, w4, hb, 0)
qlmWrk -= qlm.tri_iso_prism(LMax, massTris, t, w3, hs, 0)
qlmWrk = trs.translate_qlm(qlmWrk, [-hs, 0, 0])
if flip:
qlmWrk = trs.translate_qlm(qlmWrk, [-(hb - hs), 0, 0])
qlmWrk = rot.rotate_qlm(qlmWrk, 0, 0, np.pi)
pos = np.array(lines[4 + k].split(','), dtype=float) * fac
k += 3
if (pos == 0).all() and ('add' in lines[2 + k]):
k += 1
print('added ', shape)
qlmTot += qlmWrk
else:
print('translated ', shape)
qlmWrk = trs.translate_qlm(qlmWrk, pos)
elif shape == 'partcylinder':
line2 = [float(val) * fac for val in lines[2 + k].split(',')]
r, d, h = line2
dens = float(lines[3 + k].split(',')[0]) * 1000
phih = np.arccos(d / r)
massCyl = dens * h * phih * r**2
massTri = dens * h * d * r * np.sin(phih)
qlmWrk = qlm.annulus(LMax, massCyl, h, 0, r, 0, phih)
qlmWrk -= qlm.tri_iso_prism2(LMax, massTri, h, r, 0, phih)
pos = np.array(lines[4 + k].split(','), dtype=float) * fac
k += 3
if (pos == 0).all() and ('add' in lines[2 + k]):
k += 1
print('added ', shape)
qlmTot += qlmWrk
else:
print('translated ', shape)
qlmWrk = trs.translate_qlm(qlmWrk, pos)
elif shape == 'tetrahedron':
line2 = [float(val) * fac for val in lines[2 + k].split(',')]
x, y, z = line2
dens = float(lines[3 + k].split(',')[0]) * 1000
mass = dens * x * y * z / 6
qlmWrk = qlm.tetrahedron(LMax, mass, x, y, z)
pos = np.array(lines[4 + k].split(','), dtype=float) * fac
k += 3
if (pos == 0).all() and ('add' in lines[2 + k]):
k += 1
print('added ', shape)
qlmTot += qlmWrk
else:
print('translated ', shape)
qlmWrk = trs.translate_qlm(qlmWrk, pos)
elif shape == 'platehole':
line2 = [float(val) for val in lines[2 + k].split(',')]
r, t, theta = line2
t, r = t * fac, r * fac
theta *= np.pi / 180
dens = float(lines[3 + k].split(',')[0]) * 1000
qlmWrk = qlmA.platehole(LMax, dens, t, r, theta)
# qlmWrk = qlmN.platehole(LMax, dens, t, r, theta)
# qlmWrk = rot.rotate_qlm(qlmWrk, 0, theta, 0)
pos = np.array(lines[4 + k].split(','), dtype=float) * fac
k += 3
if (pos == 0).all() and ('add' in lines[2 + k]):
k += 1
print('added ', shape)
qlmTot += qlmWrk
else:
print('translated ', shape)
qlmWrk = trs.translate_qlm(qlmWrk, pos)
elif shape == 'cylhole':
line2 = [float(val) * fac for val in lines[2 + k].split(',')]
r, R = line2
dens = float(lines[3 + k].split(',')[0]) * 1000
qlmWrk = qlmN.steinmetz(LMax, dens, r, R)
qlmWrk = rot.rotate_qlm(qlmWrk, np.pi / 2, 0, 0)
pos = np.array(lines[4 + k].split(','), dtype=float) * fac
k += 3
if (pos == 0).all() and ('add' in lines[2 + k]):
k += 1
print('added ', shape)
qlmTot += qlmWrk
else:
print('translated ', shape)
qlmWrk = trs.translate_qlm(qlmWrk, pos)
elif shape == 'pyramid':
line2 = [float(val) * fac for val in lines[2 + k].split(',')]
x, y, z = line2
dens = float(lines[3 + k].split(',')[0]) * 1000
mass = dens * x * y * z / 3
qlmWrk = qlm.pyramid(LMax, mass, x / 2, y / 2, z)
pos = np.array(lines[4 + k].split(','), dtype=float) * fac
k += 3
if (pos == 0).all() and ('add' in lines[2 + k]):
k += 1
print('added ', shape)
qlmTot += qlmWrk
else:
print('translated ', shape)
qlmWrk = trs.translate_qlm(qlmWrk, pos)
elif shape == 'rectangle':
line2 = [float(val) * fac for val in lines[2 + k].split(',')]
x, y, z = line2
dens = float(lines[3 + k].split(',')[0]) * 1000
mass = dens * x * y * z
qlmWrk = qlm.rect_prism(LMax, mass, z, x, y, 0)
pos = np.array(lines[4 + k].split(','), dtype=float) * fac
k += 3
if (pos == 0).all() and ('add' in lines[2 + k]):
k += 1
print('added ', shape)
qlmTot += qlmWrk
else:
print('translated ', shape)
qlmWrk = trs.translate_qlm(qlmWrk, pos)
else:
print(shape, ' does not have a known set of moments')
for n in range(nlines - k):
line2 = lines[1 + k + 1]
if ('create' not in line2) and ('end' not in line2):
k += 1
else:
break
elif 'rotate' in line:
dphi = np.array(line.split('rotate')[1].split(','), dtype=float)
# Convert to radians
dphi *= np.pi / 180
print('rotated ', shape)
qlmWrk = rot.rotate_qlm(qlmWrk, dphi[0], dphi[1], dphi[2])
elif 'translate' in line:
print('translated ', shape)
dr = np.array(line.split('translate')[1].split(','), dtype=float)
dr *= fac
qlmWrk = trs.translate_qlm(qlmWrk, dr)
elif 'add' in line:
print('added ', shape)
qlmTot += qlmWrk
elif 'cmin' in line:
print('parameters in centimeters')
fac = 1e-2
elif 'inchin' in line:
print('parameters in inches')
fac = 25.4e-3
elif 'nsteps' in line:
nsteps = line.split()[-1]
elif 'load' in line:
fname = line.split('load ')[1]
fname = fname.strip()
print(fname)
qlmLoad = read_gsq(fname, filepath.replace('mpc', 'mom'))
if np.shape(qlmLoad) != np.shape(qlmWrk):
raise TypeError('Loaded part ' + fname + ' has wrong LMax')
qlmWrk = qlmLoad
shape = fname
elif 'zeroqlm' in line:
qlmTot *= 0
elif 'gettotal' in line:
qlmWrk = np.copy(qlmTot)
shape = 'Total'
elif 'puttotal' in line:
qlmTot = np.copy(qlmWrk)
shape = 'Working'
elif 'end' in line:
print('end')
break
k += 1
return qlmTot
beta = np.pi / 8 dens = 2800 # kg/m^3, 7075 T6 aluminum mc = dens * 2 * beta * (orc**2 - irc**2) * hc r3 = .10478 r2 = .06033 mtm = 39.658 htm = .20 # 20cm thickness rtm = .35 / 2 # 35cm diam d = 1.32 # m phi = 0.241 # radian dx = d * np.cos(phi) dy = d * np.sin(phi) LMax = 10 # Create some rotating test-masses arc = qlm.annulus(LMax, mc / 2, hc, irc, orc, 0, beta) arc2 = rot.rotate_qlm(arc, np.pi, 0, 0) arctot = arc + arc2 # create a test-mirror tm = qlm.cylinder(LMax, mtm, htm, rtm) tm = rot.rotate_qlm(tm, np.pi / 2, np.pi / 2, -np.pi / 2) tm = trs.translate_q2Q(tm, [dx, dy, 0]) # Figure out the force at different rotor angles nAng = 120 forces = np.zeros([nAng, 3], dtype='complex') nlm, nc, ns = mplb.torque_lm(LMax, arctot, tm) dphi = 2 * np.pi / nAng # Now rotate the cylindrical test-masses through various angles and calculate # the forces