ell
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@@ -17,7 +17,7 @@ def sph_azimuth(beta1, lam1, beta2, lam2):
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a += 2 * np.pi
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return a
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def BETA_LAMBDA(beta, lamb):
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def BETA_LAMBDA(ell, beta, lamb):
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BETA = (ell.ay**2 * np.sin(beta)**2 + ell.b**2 * np.cos(beta)**2) / (ell.Ex**2 - ell.Ey**2 * np.sin(beta)**2)
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LAMBDA = (ell.ax**2 * np.sin(lamb)**2 + ell.ay**2 * np.cos(lamb)**2) / (ell.Ex**2 - ell.Ee**2 * np.cos(lamb)**2)
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@@ -63,7 +63,7 @@ def p_coef(beta, lamb):
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BETA_, LAMBDA_, BETA__, LAMBDA__,
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E_beta, E_lamb, G_beta, G_lamb,
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E_beta_beta, E_beta_lamb, E_lamb_lamb,
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G_beta_beta, G_beta_lamb, G_lamb_lamb) = BETA_LAMBDA(beta, lamb)
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G_beta_beta, G_beta_lamb, G_lamb_lamb) = BETA_LAMBDA(ell, beta, lamb)
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p_3 = - 0.5 * (E_lamb / G)
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p_2 = (G_beta / G) - 0.5 * (E_beta / E)
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@@ -102,7 +102,7 @@ def q_coef(beta, lamb):
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BETA_, LAMBDA_, BETA__, LAMBDA__,
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E_beta, E_lamb, G_beta, G_lamb,
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E_beta_beta, E_beta_lamb, E_lamb_lamb,
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G_beta_beta, G_beta_lamb, G_lamb_lamb) = BETA_LAMBDA(beta, lamb)
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G_beta_beta, G_beta_lamb, G_lamb_lamb) = BETA_LAMBDA(ell, beta, lamb)
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q_3 = - 0.5 * (G_beta / E)
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q_2 = (E_lamb / E) - 0.5 * (G_lamb / G)
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@@ -164,7 +164,7 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
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if abs(dlamb) < 1e-15:
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beta_0 = 0.0
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else:
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(_, _, E1, G1, *_) = BETA_LAMBDA(beta_1, lamb_1)
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(_, _, E1, G1, *_) = BETA_LAMBDA(ell, beta_1, lamb_1)
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beta_0 = np.sqrt(G1 / E1) * cot(alpha0_sph)
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ode_lamb = buildODElamb()
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@@ -196,7 +196,7 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
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return False, None, None, None
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alpha0_sph = sph_azimuth(beta_1, lamb_1, beta_2, lamb_2)
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(_, _, E1, G1, *_) = BETA_LAMBDA(beta_1, lamb_1)
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(_, _, E1, G1, *_) = BETA_LAMBDA(ell, beta_1, lamb_1)
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beta_p0_sph = np.sqrt(G1 / E1) * cot(alpha0_sph)
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guesses = [
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@@ -220,7 +220,7 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
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integrand = np.zeros(N + 1)
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for i in range(N + 1):
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(_, _, Ei, Gi, *_) = BETA_LAMBDA(beta_arr_c[i], lamb_arr_c[i])
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(_, _, Ei, Gi, *_) = BETA_LAMBDA(ell, beta_arr_c[i], lamb_arr_c[i])
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integrand[i] = np.sqrt(Ei * beta_p_arr_c[i] ** 2 + Gi)
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h = abs(dlamb) / N
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@@ -253,9 +253,9 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
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beta_p_arr[i] = state[1]
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(_, _, E1, G1,
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*_) = BETA_LAMBDA(beta_arr[0], lamb_arr[0])
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*_) = BETA_LAMBDA(ell, beta_arr[0], lamb_arr[0])
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(_, _, E2, G2,
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*_) = BETA_LAMBDA(beta_arr[-1], lamb_arr[-1])
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*_) = BETA_LAMBDA(ell, beta_arr[-1], lamb_arr[-1])
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alpha_1 = arccot(np.sqrt(E1 / G1) * beta_p_arr[0])
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alpha_2 = arccot(np.sqrt(E2 / G2) * beta_p_arr[-1])
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@@ -263,7 +263,7 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
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integrand = np.zeros(N + 1)
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for i in range(N + 1):
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(_, _, Ei, Gi,
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*_) = BETA_LAMBDA(beta_arr[i], lamb_arr[i])
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*_) = BETA_LAMBDA(ell, beta_arr[i], lamb_arr[i])
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integrand[i] = np.sqrt(Ei * beta_p_arr[i] ** 2 + Gi)
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h = abs(dlamb) / N
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@@ -341,9 +341,9 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
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# Azimute
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(BETA1, LAMBDA1, E1, G1,
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*_) = BETA_LAMBDA(beta_arr[0], lamb_arr[0])
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*_) = BETA_LAMBDA(ell, beta_arr[0], lamb_arr[0])
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(BETA2, LAMBDA2, E2, G2,
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*_) = BETA_LAMBDA(beta_arr[-1], lamb_arr[-1])
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*_) = BETA_LAMBDA(ell, beta_arr[-1], lamb_arr[-1])
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alpha_1 = (np.pi / 2.0) - arccot(np.sqrt(LAMBDA1 / BETA1) * lambda_p_arr[0])
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alpha_2 = (np.pi / 2.0) - arccot(np.sqrt(LAMBDA2 / BETA2) * lambda_p_arr[-1])
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@@ -351,7 +351,7 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
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integrand = np.zeros(N + 1)
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for i in range(N + 1):
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(_, _, Ei, Gi,
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*_) = BETA_LAMBDA(beta_arr[i], lamb_arr[i])
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*_) = BETA_LAMBDA(ell, beta_arr[i], lamb_arr[i])
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integrand[i] = np.sqrt(Ei + Gi * lambda_p_arr[i] ** 2)
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h = abs(dbeta) / N
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