62 lines
2.6 KiB
Python
62 lines
2.6 KiB
Python
import numpy as np
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import ellipsoide
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import Numerische_Integration.num_int_runge_kutta as rk
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import winkelumrechnungen as wu
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import ausgaben as aus
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import GHA.rk as ghark
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# Panou, Korakitits 2019
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def gha1(ell: ellipsoide.EllipsoidTriaxial, x, y, z, alpha0, s, num):
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H = x**2 + y**2 / (1-ell.ee**2)**2 + z**2/(1-ell.ex**2)**2
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n = np.array([x/np.sqrt(H), y/((1-ell.ee**2)*np.sqrt(H)), z/((1-ell.ex**2)*np.sqrt(H))])
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beta, lamb, u = ell.cart2ell(x, y, z)
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B = ell.Ex**2 * np.cos(beta)**2 + ell.Ee**2 * np.sin(beta)**2
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L = ell.Ex**2 - ell.Ee**2 * np.cos(lamb)**2
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c1 = x**2 + y**2 + z**2 - (ell.ax**2 + ell.ay**2 + ell.b**2)
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c0 = (ell.ax**2*ell.ay**2 + ell.ax**2*ell.b**2+ell.ay**2*ell.b**2 -
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(ell.ay**2+ell.b**2)*x**2 - (ell.ax**2+ell.b**2)*y**2 - (ell.ax**2+ell.ay**2)*z**2)
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t2 = (-c1 + np.sqrt(c1**2 - 4*c0)) / 2
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t1 = c0 / t2
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F = ell.Ey**2 * np.cos(beta)**2 + ell.Ee**2 * np.sin(lamb)**2
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p1 = -np.sqrt(L/(F*t2)) * ell.ax/ell.Ex * np.sqrt(B) * np.sin(lamb)
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p2 = np.sqrt(L/(F*t2)) * ell.ay * np.cos(beta) * np.cos(lamb)
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p3 = 1 / np.sqrt(F*t2) * (ell.b*ell.Ee**2)/(2*ell.Ex) * np.sin(beta) * np.sin(2*lamb)
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p = np.array([p1, p2, p3])
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q = np.cross(n, p)
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dxds0 = p[0] * np.sin(alpha0) + q[0] * np.cos(alpha0)
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dyds0 = p[1] * np.sin(alpha0) + q[1] * np.cos(alpha0)
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dzds0 = p[2] * np.sin(alpha0) + q[2] * np.cos(alpha0)
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h = lambda dxds, dyds, dzds: dxds**2 + 1/(1-ell.ee**2)*dyds**2 + 1/(1-ell.ex**2)*dzds**2
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f1 = lambda s, x, dxds, y, dyds, z, dzds: dxds
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f2 = lambda s, x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / H * x
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f3 = lambda s, x, dxds, y, dyds, z, dzds: dyds
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f4 = lambda s, x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / H * y/(1-ell.ee**2)
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f5 = lambda s, x, dxds, y, dyds, z, dzds: dzds
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f6 = lambda s, x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / H * z/(1-ell.ex**2)
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funktionswerte = rk.verfahren([f1, f2, f3, f4, f5, f6], [0, x, dxds0, y, dyds0, z, dzds0], s, num)
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return funktionswerte
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if __name__ == "__main__":
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ell = ellipsoide.EllipsoidTriaxial.init_name("Eitschberger1978")
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ellbi = ellipsoide.EllipsoidTriaxial.init_name("Bessel-biaxial")
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re = ellipsoide.EllipsoidBiaxial.init_name("Bessel")
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x0 = 5672455.1954766
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y0 = 2698193.7242382686
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z0 = 1103177.6450055107
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alpha0 = wu.gms2rad([20, 0, 0])
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s = 10000
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num = 10000
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werteTri = gha1(ellbi, x0, y0, z0, alpha0, s, num)
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print(aus.xyz(werteTri[-1][1], werteTri[-1][3], werteTri[-1][5], 8))
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werteBi = ghark.gha1(re, x0, y0, z0, alpha0, s, num)
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print(aus.xyz(werteBi[0], werteBi[1], werteBi[2], 8)) |