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analytisch funktioniert noch nicht

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Hendrik Möllersmann
2025-11-04 14:18:17 +01:00
parent 610ea3dc28
commit 1c56b089f2
3 changed files with 92 additions and 31 deletions
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96
GHA_triaxial/panou.py
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@@ -4,6 +4,8 @@ import Numerische_Integration.num_int_runge_kutta as rk
import winkelumrechnungen as wu
import ausgaben as aus
import GHA.rk as ghark
from scipy.special import factorial as fact
from math import comb
# Panou, Korakitits 2019
@@ -35,7 +37,9 @@ def p_q(ell: ellipsoide.EllipsoidTriaxial, x, y, z):
# 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.cross(n, p)
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}
@@ -98,30 +102,71 @@ def gha1_ana(ell: ellipsoide.EllipsoidTriaxial, x, y, z, alpha0, s, maxM):
:param maxM:
:return:
"""
Hsp = []
# H Ableitungen (7)
hsq = []
# h Ableitungen (7)
hHst = []
# h/H Ableitungen (6)
xsm = [x]
ysm = [y]
zsm = [z]
x_m = [x]
y_m = [y]
z_m = [z]
# erste Ableitungen (7-8)
sqrtH = np.sqrt(ell.H(x, y, z))
n = np.array([x / sqrtH,
y / ((1-ell.ee**2) * sqrtH),
z / ((1-ell.ex**2) * sqrtH)])
u, v = ell.cart2para(x, y, z)
G = np.sqrt(1 - ell.ex**2 * np.cos(u)**2 - ell.ee**2 * np.sin(u)**2 * np.sin(v)**2)
q = np.array([-1/G * np.sin(u) * np.cos(v),
-1/G * np.sqrt(1-ell.ee**2) * np.sin(u) * np.sin(v),
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]])
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))
# H Ableitungen (7)
H_ = lambda p: np.sum([comb(p, i) * (x_m[p - i] * x_m[i] +
1 / (1-ell.ee**2) ** 2 * y_m[p-i] * y_m[i] +
1 / (1-ell.ex**2) ** 2 * z_m[p-i] * z_m[i]) for i in range(0, p+1)])
# 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)])
# 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)]))
# xm, ym, zm Ableitungen (6)
am = []
bm = []
cm = []
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)])
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))
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 am:
for a in a_m:
x_s = x_s * s + a
y_s = 0
for b in bm:
for b in b_m:
y_s = y_s * s + b
z_s = 0
for c in cm:
for c in c_m:
z_s = z_s * s + c
return x_s, y_s, z_s
pass
@@ -133,12 +178,15 @@ if __name__ == "__main__":
y0 = 2698193.7242382686
z0 = 1103177.6450055107
alpha0 = wu.gms2rad([20, 0, 0])
s = 10000
num = 10000
# werteTri = gha1_num(ellbi, x0, y0, z0, alpha0, s, num)
# print(aus.xyz(werteTri[-1][1], werteTri[-1][3], werteTri[-1][5], 8))
# checkLiouville(ell, werteTri)
# werteBi = ghark.gha1(re, x0, y0, z0, alpha0, s, num)
# print(aus.xyz(werteBi[0], werteBi[1], werteBi[2], 8))
s = 100
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)
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))
gha1_ana(ell, x0, y0, z0, alpha0, s, 7)
werteAna = gha1_ana(ell, x0, y0, z0, alpha0, s, 7)
print(aus.xyz(werteAna[0], werteAna[1], werteAna[2], 8))

20
ellipsoide.py
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@@ -267,15 +267,23 @@ class EllipsoidTriaxial:
:param z:
:return:
"""
if z*np.sqrt(1-self.ee**2) <= np.sqrt(x**2 * (1-self.ee**2)+y**2) * np.sqrt(1-self.ex**2):
u = np.arctan(z*np.sqrt(1-self.ee**2) / np.sqrt(x**2 * (1-self.ee**2)+y**2) * np.sqrt(1-self.ex**2))
u_check1 = z*np.sqrt(1 - self.ee**2)
u_check2 = np.sqrt(x**2 * (1-self.ee**2) + y**2) * np.sqrt(1-self.ex**2)
if u_check1 <= u_check2:
u = np.arctan(u_check1 / u_check2)
else:
u = np.arctan(np.sqrt(x**2 * (1-self.ee**2)+y**2) * np.sqrt(1-self.ex**2) / z*np.sqrt(1-self.ee**2))
u = np.pi/2 * np.arctan(u_check2 / u_check1)
if y <= x*np.sqrt(1-self.ee**2):
v = 2*np.arctan(y/(x*np.sqrt(1-self.ee**2) + np.sqrt(x**2*(1-self.ee**2)+y**2)))
v_check1 = y
v_check2 = x*np.sqrt(1-self.ee**2)
if v_check1 <= v_check2:
v = 2 * np.arctan(v_check1 / (v_check2 + np.sqrt(x**2*(1-self.ee**2)+y**2)))
else:
v = np.pi/2 - 2*np.arctan(x*np.sqrt(1-self.ee**2) / (y + np.sqrt(x**2*(1-self.ee**2)+y**2)))
v = np.pi/2 - 2 * np.arctan(v_check2 / (v_check1 + np.sqrt(x**2*(1-self.ee**2)+y**2)))
return u, v
def H(self, x, y, z):
return x**2 + y**2/(1-self.ee**2)**2 + z**2/(1-self.ex**2)**2
if __name__ == "__main__":

7
test.py
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@@ -1,4 +1,6 @@
import numpy as np
from scipy.special import factorial as fact
from math import comb
J = np.array([
[2, 3, 0],
@@ -21,4 +23,7 @@ res_row = xi[None, :] - xi[None, :] @ J
print("Spaltenvektor:")
print(res_col[0,0])
print("Zeilenvektor:")
print(res_row)
print(res_row)
t = 5
l = 2
print(fact(t+1-l) / (fact(t+1-l) * fact(l-1)), comb(l-1, t+1-l))