174 lines
5.7 KiB
Python
174 lines
5.7 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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from scipy.special import factorial as fact
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from math import comb
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# Panou, Korakitits 2019
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def gha1_num(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, num):
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phi, lamb, h = ell.cart2geod("ligas3", point)
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x, y, z = ell.geod2cart(phi, lamb, 0)
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values = ell.p_q(x, y, z)
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H = values["H"]
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p = values["p"]
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q = values["q"]
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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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def checkLiouville(ell: ellipsoide.EllipsoidTriaxial, points):
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constantValues = []
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for point in points:
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x = point[1]
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dxds = point[2]
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y = point[3]
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dyds = point[4]
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z = point[5]
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dzds = point[6]
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values = ell.p_q(x, y, z)
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p = values["p"]
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q = values["q"]
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t1 = values["t1"]
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t2 = values["t2"]
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P = p[0]*dxds + p[1]*dyds + p[2]*dzds
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Q = q[0]*dxds + q[1]*dyds + q[2]*dzds
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alpha = np.arctan(P/Q)
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c = ell.ay**2 - (t1 * np.sin(alpha)**2 + t2 * np.cos(alpha)**2)
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constantValues.append(c)
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pass
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def gha1_ana(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, maxM):
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"""
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Panou, Korakitits 2020, 5ff.
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:param ell:
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:param x:
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:param y:
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:param z:
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:param alpha0:
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:param s:
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:param maxM:
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:return:
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"""
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x, y, z = point
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x_m = [x]
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y_m = [y]
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z_m = [z]
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# erste Ableitungen (7-8)
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sqrtH = np.sqrt(ell.p_q(x, y, z)["H"])
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n = np.array([x / sqrtH,
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y / ((1-ell.ee**2) * sqrtH),
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z / ((1-ell.ex**2) * sqrtH)])
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u, v = ell.cart2para(np.array([x, y, z]))
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G = np.sqrt(1 - ell.ex**2 * np.cos(u)**2 - ell.ee**2 * np.sin(u)**2 * np.sin(v)**2)
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q = np.array([-1/G * np.sin(u) * np.cos(v),
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-1/G * np.sqrt(1-ell.ee**2) * np.sin(u) * np.sin(v),
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1/G * np.sqrt(1-ell.ex**2) * np.cos(u)])
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p = np.array([q[1]*n[2] - q[2]*n[1],
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q[2]*n[0] - q[0]*n[2],
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q[0]*n[1] - q[1]*n[0]])
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x_m.append(p[0] * np.sin(alpha0) + q[0] * np.cos(alpha0))
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y_m.append(p[1] * np.sin(alpha0) + q[1] * np.cos(alpha0))
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z_m.append(p[2] * np.sin(alpha0) + q[2] * np.cos(alpha0))
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# H Ableitungen (7)
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H_ = lambda p: np.sum([comb(p, i) * (x_m[p - i] * x_m[i] +
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1 / (1-ell.ee**2) ** 2 * y_m[p-i] * y_m[i] +
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1 / (1-ell.ex**2) ** 2 * z_m[p-i] * z_m[i]) for i in range(0, p+1)])
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# h Ableitungen (7)
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h_ = lambda q: np.sum([comb(q, j) * (x_m[q-j+1] * x_m[j+1] +
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1 / (1 - ell.ee ** 2) * y_m[q-j+1] * y_m[j+1] +
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1 / (1 - ell.ex ** 2) * z_m[q-j+1] * z_m[j+1]) for j in range(0, q+1)])
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# h/H Ableitungen (6)
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hH_ = lambda t: 1/H_(0) * (h_(t) - fact(t) *
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np.sum([H_(t+1-l) / (fact(t+1-l) * fact(l-1)) * hH_t[l-1] for l in range(1, t+1)]))
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# xm, ym, zm Ableitungen (6)
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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)])
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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)])
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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)])
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hH_t = []
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a_m = []
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b_m = []
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c_m = []
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for m in range(0, maxM+1):
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if m >= 2:
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hH_t.append(hH_(m-2))
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x_m.append(x_(m))
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y_m.append(y_(m))
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z_m.append(z_(m))
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a_m.append(x_m[m] / fact(m))
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b_m.append(y_m[m] / fact(m))
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c_m.append(z_m[m] / fact(m))
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# am, bm, cm (6)
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x_s = 0
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for a in reversed(a_m):
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x_s = x_s * s + a
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y_s = 0
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for b in reversed(b_m):
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y_s = y_s * s + b
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z_s = 0
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for c in reversed(c_m):
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z_s = z_s * s + c
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return x_s, y_s, z_s
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pass
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if __name__ == "__main__":
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# ell = ellipsoide.EllipsoidTriaxial.init_name("Eitschberger1978")
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ell = ellipsoide.EllipsoidTriaxial.init_name("BursaSima1980")
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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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# Panou 2013, 7, Table 1, beta0=60°
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beta1 = wu.deg2rad(60)
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lamb1 = wu.deg2rad(0)
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beta2 = wu.deg2rad(60)
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lamb2 = wu.deg2rad(175)
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P1 = ell.ell2cart2(wu.deg2rad(60), wu.deg2rad(0))
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P2 = ell.ell2cart2(wu.deg2rad(60), wu.deg2rad(175))
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para1 = ell.cart2para(P1)
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para2 = ell.cart2para(P2)
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cart1 = ell.para2cart(para1[0], para1[1])
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cart2 = ell.para2cart(para2[0], para2[1])
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ell11 = ell.cart2ell2(P1)
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ell21 = ell.cart2ell2(P2)
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ell1 = ell.cart2ell2(cart1)
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ell2 = ell.cart2ell2(cart2)
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c = 0.06207487624
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alpha0 = wu.gms2rad([2, 52, 26.2393])
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alpha1 = wu.gms2rad([177, 4, 13.6373])
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s = 6705715.1610
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pass
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P2_num = gha1_num(ell, P1, alpha0, s, 1000)
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P2_ana = gha1_ana(ell, P1, alpha0, s, 70)
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pass |