Umrechnung alpha, Näherungslösung GHA 1

GHA_triaxial/approx_gha1.py

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+import numpy as np
+from numpy import sin, cos, arcsin, arccos, arctan2
+from ellipsoide import EllipsoidTriaxial
+import matplotlib.pyplot as plt
+from panou import louville_constant, func_sigma_ell, gha1_ana
+import plotly.graph_objects as go
+import winkelumrechnungen as wu
+
+def gha1(ell: EllipsoidTriaxial, p0: np.ndarray, alpha0: float, s: float, ds: int):
+    l0 = louville_constant(ell, p0, alpha0)
+    points = [p0]
+    alphas = [alpha0]
+    s_curr = 0.0
+    while s_curr < s:
+        ds_step = min(ds, s - s_curr)
+        if ds_step < 1e-8:
+            break
+        p1 = points[-1]
+        alpha1 = alphas[-1]
+        x1, y1, z1 = p1
+        sigma = func_sigma_ell(ell, x1, y1, z1, alpha1)
+        p2 = p1 + ds_step * sigma
+        p2, _, _, _ = ell.cartonell(p2)
+        ds_step = np.linalg.norm(p2 - p1)
+
+        points.append(p2)
+        dalpha = 1e-6
+        l2 = louville_constant(ell, p2, alpha1)
+        dl_dalpha = (louville_constant(ell, p2, alpha1+dalpha) - l2) / dalpha
+        alpha2 = alpha1 + (l0 - l2) / dl_dalpha
+        alphas.append(alpha2)
+        s_curr += ds_step
+    return points[-1], alphas[-1], np.array(points)
+
+def show_points(points, p0, p1):
+    fig = go.Figure()
+
+    fig.add_scatter3d(x=points[:, 0], y=points[:, 1], z=points[:, 2],
+                      mode='lines', line=dict(color="red", width=3), name="Approx")
+    fig.add_scatter3d(x=[p0[0]], y=[p0[1]], z=[p0[2]],
+                      mode='markers', marker=dict(color="green"), name="P0")
+    fig.add_scatter3d(x=[p1[0]], y=[p1[1]], z=[p1[2]],
+                      mode='markers', marker=dict(color="green"), name="P1")
+
+    fig.update_layout(
+        scene=dict(xaxis_title='X [km]',
+                   yaxis_title='Y [km]',
+                   zaxis_title='Z [km]',
+                   aspectmode='data'),
+        title="CHAMP")
+
+    fig.show()
+
+
+if __name__ == '__main__':
+    ell = EllipsoidTriaxial.init_name("BursaSima1980round")
+    P0 = ell.para2cart(0, 0)
+    alpha0 = wu.deg2rad(90)
+    s = 1000000
+    P1_ana, alpha1_ana = gha1_ana(ell, P0, alpha0, s, 60, maxPartCircum=32)
+    P1_app, alpha1_app, points = gha1(ell, P0, alpha0, s, 5000)
+    show_points(points, P0, P1_ana)
+    print(np.linalg.norm(P1_app - P1_ana))