Aufgeräumt, Grundkonstrukt analytische Lösung
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@@ -7,28 +7,44 @@ 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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def p_q(ell: ellipsoide.EllipsoidTriaxial, x, y, z):
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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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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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carts = ell.ell2cart(beta, lamb, u)
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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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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 - (
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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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t2e = ell.ax ** 2 * np.sin(lamb) ** 2 + ell.ay ** 2 * np.cos(lamb) ** 2
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t1e = ell.ay ** 2 * np.sin(beta) ** 2 + ell.b ** 2 * np.cos(beta) ** 2
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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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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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# p1 = -np.sign(y) * np.sqrt(L / (F * t2)) * ell.ax / (ell.Ex * ell.Ee) * np.sqrt(B) * np.sqrt(t2 - ell.ay ** 2)
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# p2 = np.sign(x) * np.sqrt(L / (F * t2)) * ell.ay / (ell.Ey * ell.Ee) * np.sqrt((ell.ay ** 2 - t1) * (ell.ax ** 2 - t2))
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# p3 = np.sign(x) * np.sign(y) * np.sign(z) * 1 / np.sqrt(F * t2) * ell.b / (ell.Ex * ell.Ey) * np.sqrt(
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# (t1 - ell.b ** 2) * (t2 - ell.ay ** 2) * (ell.ax ** 2 - t2))
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p = np.array([p1, p2, p3])
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q = np.cross(n, p)
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return {"H": H, "n": n, "beta": beta, "lamb": lamb, "u": u, "B": B, "L": L, "c1": c1, "c0": c0, "t1": t1, "t2": t2,
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"F": F, "p": p, "q": q}
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def gha1_num(ell: ellipsoide.EllipsoidTriaxial, x, y, z, alpha0, s, num):
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values = p_q(ell, 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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@@ -45,6 +61,69 @@ def gha1(ell: ellipsoide.EllipsoidTriaxial, x, y, z, alpha0, s, num):
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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 = p_q(ell, 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, x, y, z, 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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Hsp = []
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# H Ableitungen (7)
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hsq = []
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# h Ableitungen (7)
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hHst = []
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# h/H Ableitungen (6)
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xsm = [x]
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ysm = [y]
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zsm = [z]
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# erste Ableitungen (7-8)
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# xm, ym, zm Ableitungen (6)
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am = []
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bm = []
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cm = []
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# am, bm, cm (6)
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x_s = 0
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for a in am:
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x_s = x_s * s + a
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y_s = 0
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for b in bm:
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y_s = y_s * s + b
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z_s = 0
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for c in cm:
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z_s = z_s * s + c
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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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@@ -56,7 +135,10 @@ if __name__ == "__main__":
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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))
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# werteTri = gha1_num(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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# checkLiouville(ell, werteTri)
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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))
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gha1_ana(ell, x0, y0, z0, alpha0, s, 7)
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