37 lines
1.2 KiB
Python
37 lines
1.2 KiB
Python
from typing import Tuple
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import scipy as sp
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from ellipsoid_biaxial import EllipsoidBiaxial
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from numpy import *
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def gha1(re: EllipsoidBiaxial, phi0: float, lamb0: float, alpha0:float, s: float) -> Tuple[float, float, float]:
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"""
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Berechnung der 1.GHA auf einem Rotationsellipsoid nach Bessel
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:param re:
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:param phi0:
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:param lamb0:
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:param alpha0:
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:param s:
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:return:
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"""
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psi0 = re.phi2psi(phi0)
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clairant = arcsin(cos(psi0) * sin(alpha0))
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sigma0 = arcsin(sin(psi0) / cos(clairant))
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sqrt_sigma = lambda sigma: sqrt(1 + re.e_ ** 2 * cos(clairant) ** 2 * sin(sigma) ** 2)
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int_sqrt_sigma = lambda sigma: sp.integrate.quad(sqrt_sigma, sigma0, sigma)[0]
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f_sigma1_i = lambda sigma1_i: (int_sqrt_sigma(sigma1_i) - s / re.b)
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sigma1_0 = sigma0 + s / re.a
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sigma1 = sp.optimize.newton(f_sigma1_i, sigma1_0)
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psi1 = arcsin(cos(clairant) * sin(sigma1))
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phi1 = re.psi2phi(psi1)
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alpha1 = arcsin(sin(clairant) / cos(psi1))
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f_d_lambda = lambda sigma: sin(clairant) * sqrt_sigma(sigma) / (1 - cos(clairant) ** 2 * sin(sigma) ** 2)
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d_lambda = sqrt(1-re.e**2) * sp.integrate.quad(f_d_lambda, sigma0, sigma1)[0]
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lamb1 = lamb0 + d_lambda
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return phi1, lamb1, alpha1
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