wip theodorsen eval

data/theodorsen.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+# RK4 (dx/ds = f(x, s))
+def rk4(x0: float, s0: float, sf: float, ds: float, f: callable):
+    s = np.arange(s0, sf, ds)
+    x = np.zeros(len(s))
+    x[0] = x0
+
+    for i in range(1, len(s)):
+        k1 = ds * f(x[i-1], s[i-1])
+        k2 = ds * f(x[i-1] + 0.5 * k1, s[i-1] + 0.5 * ds)
+        k3 = ds * f(x[i-1] + 0.5 * k2, s[i-1] + 0.5 * ds)
+        k4 = ds * f(x[i-1] + k3, s[i-1] + ds)
+        x[i] = x[i-1] + (k1 + 2*k2 + 2*k3 + k4) / 6
+
+    return s, x
+
+# Two point central difference
+def derivative(f, x):
+    EPS_sqrt_f = np.sqrt(1.19209e-07)
+    return (f(x + EPS_sqrt_f) - f(x - EPS_sqrt_f)) / (2 * EPS_sqrt_f)
+
+# Jone approximation of Wagner function
+b0 = 1
+b1 = -0.165
+b2 = -0.335
+beta_1 = 0.0455
+beta_2 = 0.3
+
+# UVLM parameters
+u_inf = 1 # freestream
+b = 5 # wing total span
+a = 1 # wing chord
+
+def pitch(t): return 0
+def heave(t): return np.sin(0.2 * t)
+
+# Define the function w(s)
+def w(s: float): return u_inf * pitch(s) + derivative(heave, s) + b * (0.5 - a) * derivative(pitch, s)
+
+def dx1ds(x1: callable, s: float): return b1 * beta_1 * w(s) - beta_1 * x1(s)
+def dx2ds(x2: callable, s: float): return b2 * beta_2 * w(s) - beta_2 * x2(s)
+
+# # Initial condition
+# x0 = # Your initial value for x_aug1 at s = s0
+# s0 = # Your start value for s
+# sf = # Your end value for s
+# ds = # Your step size for s
+
+# # Solve the differential equation
+# s, x_aug1 = rk4(x0, s0, sf, ds)
+
+# # Plot the solution
+# plt.plot(s, x_aug1)
+# plt.xlabel('s')
+# plt.ylabel('x_aug1(s)')
+# plt.title('Solution of the differential equation')
+# plt.show()