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analytisch funktioniert, p_q in ellisoid

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Hendrik Möllersmann
2025-11-04 15:47:44 +01:00
parent ff81093d34
commit 4e85eef5d7
2 changed files with 73 additions and 63 deletions
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79
GHA_triaxial/panou.py
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@@ -9,42 +9,9 @@ from math import comb
# Panou, Korakitits 2019
def p_q(ell: ellipsoide.EllipsoidTriaxial, x, y, z):
H = x ** 2 + y ** 2 / (1 - ell.ee ** 2) ** 2 + z ** 2 / (1 - ell.ex ** 2) ** 2
n = np.array([x / np.sqrt(H), y / ((1 - ell.ee ** 2) * np.sqrt(H)), z / ((1 - ell.ex ** 2) * np.sqrt(H))])
beta, lamb, u = ell.cart2ell(x, y, z)
carts = ell.ell2cart(beta, lamb, u)
B = ell.Ex ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(beta) ** 2
L = ell.Ex ** 2 - ell.Ee ** 2 * np.cos(lamb) ** 2
c1 = x ** 2 + y ** 2 + z ** 2 - (ell.ax ** 2 + ell.ay ** 2 + ell.b ** 2)
c0 = (ell.ax ** 2 * ell.ay ** 2 + ell.ax ** 2 * ell.b ** 2 + ell.ay ** 2 * ell.b ** 2 -
(ell.ay ** 2 + ell.b ** 2) * x ** 2 - (ell.ax ** 2 + ell.b ** 2) * y ** 2 - (
ell.ax ** 2 + ell.ay ** 2) * z ** 2)
t2 = (-c1 + np.sqrt(c1**2 - 4*c0)) / 2
t1 = c0 / t2
t2e = ell.ax ** 2 * np.sin(lamb) ** 2 + ell.ay ** 2 * np.cos(lamb) ** 2
t1e = ell.ay ** 2 * np.sin(beta) ** 2 + ell.b ** 2 * np.cos(beta) ** 2
F = ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2
p1 = -np.sqrt(L / (F * t2)) * ell.ax / ell.Ex * np.sqrt(B) * np.sin(lamb)
p2 = np.sqrt(L / (F * t2)) * ell.ay * np.cos(beta) * np.cos(lamb)
p3 = 1 / np.sqrt(F * t2) * (ell.b * ell.Ee ** 2) / (2 * ell.Ex) * np.sin(beta) * np.sin(2 * lamb)
# p1 = -np.sign(y) * np.sqrt(L / (F * t2)) * ell.ax / (ell.Ex * ell.Ee) * np.sqrt(B) * np.sqrt(t2 - ell.ay ** 2)
# p2 = np.sign(x) * np.sqrt(L / (F * t2)) * ell.ay / (ell.Ey * ell.Ee) * np.sqrt((ell.ay ** 2 - t1) * (ell.ax ** 2 - t2))
# p3 = np.sign(x) * np.sign(y) * np.sign(z) * 1 / np.sqrt(F * t2) * ell.b / (ell.Ex * ell.Ey) * np.sqrt(
# (t1 - ell.b ** 2) * (t2 - ell.ay ** 2) * (ell.ax ** 2 - t2))
p = np.array([p1, p2, p3])
q = np.array([n[1]*p[2]-n[2]*p[1],
n[2]*p[0]-n[0]*p[2],
n[1]*p[1]-n[1]*p[0]])
return {"H": H, "n": n, "beta": beta, "lamb": lamb, "u": u, "B": B, "L": L, "c1": c1, "c0": c0, "t1": t1, "t2": t2,
"F": F, "p": p, "q": q}
def gha1_num(ell: ellipsoide.EllipsoidTriaxial, x, y, z, alpha0, s, num):
values = p_q(ell, x, y, z)
values = ell.p_q(x, y, z)
H = values["H"]
p = values["p"]
q = values["q"]
@@ -75,7 +42,7 @@ def checkLiouville(ell: ellipsoide.EllipsoidTriaxial, points):
z = point[5]
dzds = point[6]
values = p_q(ell, x, y, z)
values = ell.p_q(x, y, z)
p = values["p"]
q = values["q"]
t1 = values["t1"]
@@ -107,7 +74,7 @@ def gha1_ana(ell: ellipsoide.EllipsoidTriaxial, x, y, z, alpha0, s, maxM):
z_m = [z]
# erste Ableitungen (7-8)
sqrtH = np.sqrt(ell.H(x, y, z))
sqrtH = np.sqrt(ell.p_q(x, y, z)["H"])
n = np.array([x / sqrtH,
y / ((1-ell.ee**2) * sqrtH),
z / ((1-ell.ex**2) * sqrtH)])
@@ -118,7 +85,7 @@ def gha1_ana(ell: ellipsoide.EllipsoidTriaxial, x, y, z, alpha0, s, maxM):
1/G * np.sqrt(1-ell.ex**2) * np.cos(u)])
p = np.array([q[1]*n[2] - q[2]*n[1],
q[2]*n[0] - q[0]*n[2],
q[1]*n[1] - q[1]*n[0]])
q[0]*n[1] - q[1]*n[0]])
x_m.append(p[0] * np.sin(alpha0) + q[0] * np.cos(alpha0))
y_m.append(p[1] * np.sin(alpha0) + q[1] * np.cos(alpha0))
z_m.append(p[2] * np.sin(alpha0) + q[2] * np.cos(alpha0))
@@ -130,40 +97,41 @@ def gha1_ana(ell: ellipsoide.EllipsoidTriaxial, x, y, z, alpha0, s, maxM):
# h Ableitungen (7)
h_ = lambda q: np.sum([comb(q, j) * (x_m[q-j+1] * x_m[j+1] +
1 / (1 - ell.ee ** 2) ** 2 * y_m[q-j+1] * y_m[j+1] +
1 / (1 - ell.ex ** 2) ** 2 * z_m[q-j+1] * z_m[j+1]) for j in range(0, q + 1)])
1 / (1 - ell.ee ** 2) * y_m[q-j+1] * y_m[j+1] +
1 / (1 - ell.ex ** 2) * z_m[q-j+1] * z_m[j+1]) for j in range(0, q+1)])
# h/H Ableitungen (6)
hH_ = lambda t: 1/H_(0) * (h_(t) - fact(t) *
np.sum([H_(t+1-l)/(fact(t+1-l)*fact(l-1))*hH_t[l-1] for l in range(1, t+1)]))
np.sum([H_(t+1-l) / (fact(t+1-l) * fact(l-1)) * hH_t[l-1] for l in range(1, t+1)]))
# xm, ym, zm Ableitungen (6)
x_ = lambda m: -np.sum([comb(m-2, k) * hH_t[m-2-k] * x_m[k] for k in range(0, m-2+1)])
y_ = lambda m: -1/(1-ell.ee**2) * np.sum([comb(m-2, k) * hH_t[m-2-k] * y_m[k] for k in range(0, m-2+1)])
z_ = lambda m: -1/(1-ell.ex**2) * np.sum([comb(m-2, k) * hH_t[m-2-k] * z_m[k] for k in range(0, m-2+1)])
y_ = lambda m: -1 / (1-ell.ee**2) * np.sum([comb(m-2, k) * hH_t[m-2-k] * y_m[k] for k in range(0, m-2+1)])
z_ = lambda m: -1 / (1-ell.ex**2) * np.sum([comb(m-2, k) * hH_t[m-2-k] * z_m[k] for k in range(0, m-2+1)])
hH_t = []
a_m = []
b_m = []
c_m = []
for m in range(2, maxM+1):
hH_t.append(hH_(m-2))
x_m.append(x_(m))
for m in range(0, maxM+1):
if m >= 2:
hH_t.append(hH_(m-2))
x_m.append(x_(m))
y_m.append(y_(m))
z_m.append(z_(m))
a_m.append(x_m[m] / fact(m))
y_m.append(y_(m))
b_m.append(y_m[m] / fact(m))
z_m.append(z_(m))
c_m.append(z_m[m] / fact(m))
# am, bm, cm (6)
x_s = 0
for a in a_m:
for a in reversed(a_m):
x_s = x_s * s + a
y_s = 0
for b in b_m:
for b in reversed(b_m):
y_s = y_s * s + b
z_s = 0
for c in c_m:
for c in reversed(c_m):
z_s = z_s * s + c
return x_s, y_s, z_s
@@ -178,15 +146,16 @@ if __name__ == "__main__":
y0 = 2698193.7242382686
z0 = 1103177.6450055107
alpha0 = wu.gms2rad([20, 0, 0])
s = 100
s = 500000
num = 100
werteTri = gha1_num(ellbi, x0, y0, z0, alpha0, s, num)
print(aus.xyz(werteTri[-1][1], werteTri[-1][3], werteTri[-1][5], 8))
print(np.sqrt((x0-werteTri[-1][1])**2+(y0-werteTri[-1][3])**2+(z0-werteTri[-1][5])**2))
checkLiouville(ell, werteTri)
print("Distanz Triaxial Numerisch", np.sqrt((x0-werteTri[-1][1])**2+(y0-werteTri[-1][3])**2+(z0-werteTri[-1][5])**2))
# checkLiouville(ell, werteTri)
werteBi = ghark.gha1(re, x0, y0, z0, alpha0, s, num)
print(aus.xyz(werteBi[0], werteBi[1], werteBi[2], 8))
print(np.sqrt((x0-werteBi[0])**2+(y0-werteBi[1])**2+(z0-werteBi[2])**2))
print("Distanz Biaxial", np.sqrt((x0-werteBi[0])**2+(y0-werteBi[1])**2+(z0-werteBi[2])**2))
werteAna = gha1_ana(ell, x0, y0, z0, alpha0, s, 7)
print(aus.xyz(werteAna[0], werteAna[1], werteAna[2], 8))
print(aus.xyz(werteAna[0], werteAna[1], werteAna[2], 8))
print("Distanz Triaxial Analytisch", np.sqrt((x0-werteAna[0])**2+(y0-werteAna[1])**2+(z0-werteAna[2])**2))