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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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57
ellipsoide.py
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@@ -2,6 +2,7 @@ import numpy as np
import winkelumrechnungen as wu
import ausgaben as aus
import jacobian_Ligas
from GHA_triaxial.panou import p_q
class EllipsoidBiaxial:
@@ -282,19 +283,57 @@ class EllipsoidTriaxial:
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
def p_q(self, x, y, z):
H = x ** 2 + y ** 2 / (1 - self.ee ** 2) ** 2 + z ** 2 / (1 - self.ex ** 2) ** 2
n = np.array([x / np.sqrt(H), y / ((1 - self.ee ** 2) * np.sqrt(H)), z / ((1 - ell.ex ** 2) * np.sqrt(H))])
beta, lamb, u = self.cart2ell(x, y, z)
carts = self.ell2cart(beta, lamb, u)
B = self.Ex ** 2 * np.cos(beta) ** 2 + self.Ee ** 2 * np.sin(beta) ** 2
L = self.Ex ** 2 - self.Ee ** 2 * np.cos(lamb) ** 2
c1 = x ** 2 + y ** 2 + z ** 2 - (self.ax ** 2 + self.ay ** 2 + self.b ** 2)
c0 = (self.ax ** 2 * self.ay ** 2 + self.ax ** 2 * self.b ** 2 + self.ay ** 2 * self.b ** 2 -
(self.ay ** 2 + self.b ** 2) * x ** 2 - (self.ax ** 2 + self.b ** 2) * y ** 2 - (
self.ax ** 2 + self.ay ** 2) * z ** 2)
t2 = (-c1 + np.sqrt(c1 ** 2 - 4 * c0)) / 2
t1 = c0 / t2
t2e = self.ax ** 2 * np.sin(lamb) ** 2 + self.ay ** 2 * np.cos(lamb) ** 2
t1e = self.ay ** 2 * np.sin(beta) ** 2 + self.b ** 2 * np.cos(beta) ** 2
F = self.Ey ** 2 * np.cos(beta) ** 2 + self.Ee ** 2 * np.sin(lamb) ** 2
p1 = -np.sqrt(L / (F * t2)) * self.ax / self.Ex * np.sqrt(B) * np.sin(lamb)
p2 = np.sqrt(L / (F * t2)) * self.ay * np.cos(beta) * np.cos(lamb)
p3 = 1 / np.sqrt(F * t2) * (self.b * self.Ee ** 2) / (2 * self.Ex) * np.sin(beta) * np.sin(2 * lamb)
# p1 = -np.sign(y) * np.sqrt(L / (F * t2)) * self.ax / (self.Ex * self.Ee) * np.sqrt(B) * np.sqrt(t2 - self.ay ** 2)
# p2 = np.sign(x) * np.sqrt(L / (F * t2)) * self.ay / (self.Ey * self.Ee) * np.sqrt((ell.ay ** 2 - t1) * (self.ax ** 2 - t2))
# p3 = np.sign(x) * np.sign(y) * np.sign(z) * 1 / np.sqrt(F * t2) * self.b / (self.Ex * self.Ey) * np.sqrt(
# (t1 - self.b ** 2) * (t2 - self.ay ** 2) * (self.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 louvilleConstant(ell, x, y, z):
values = p_q(ell, x, y, z)
pass
if __name__ == "__main__":
ellips = EllipsoidTriaxial.init_name("Eitschberger1978")
carts = ellips.ell2cart(wu.deg2rad(10), wu.deg2rad(30), 6378172)
ells = ellips.cart2ell(carts[0], carts[1], carts[2])
print(aus.gms("beta", ells[0], 3), aus.gms("lambda", ells[1], 3), "u =", ells[2])
ells2 = ellips.cart2ell(5712200, 2663400, 1106000)
carts2 = ellips.ell2cart(ells2[0], ells2[1], ells2[2])
print(aus.xyz(carts2[0], carts2[1], carts2[2], 10))
# carts = ellips.ell2cart(wu.deg2rad(10), wu.deg2rad(30), 6378172)
# ells = ellips.cart2ell(carts[0], carts[1], carts[2])
# print(aus.gms("beta", ells[0], 3), aus.gms("lambda", ells[1], 3), "u =", ells[2])
# ells2 = ellips.cart2ell(5712200, 2663400, 1106000)
# carts2 = ellips.ell2cart(ells2[0], ells2[1], ells2[2])
# print(aus.xyz(carts2[0], carts2[1], carts2[2], 10))
# stellen = 20
# geod1 = ellips.cart2geod("ligas1", 5712200, 2663400, 1106000)
@@ -312,4 +351,6 @@ if __name__ == "__main__":
# test_cart = ellips.geod2cart(0.175, 0.444, 100)
# print(aus.xyz(test_cart[0], test_cart[1], test_cart[2], 10))
ellips.louvilleConstant(5712200, 2663400, 1106000)
pass