Create app.py

app.py

@@ -0,0 +1,55 @@
+import streamlit as st
+import numpy as np
+from scipy.integrate import odeint
+import matplotlib.pyplot as plt
+
+class Pendulum:
+    def __init__(self, length, gravity):
+        self.L = length
+        self.g = gravity
+    
+    def derivatives(self, state, t):
+        theta, omega = state
+        dydt = [omega, -self.g/self.L * np.sin(theta)]
+        return dydt
+    
+    def simulate(self, initial_angle, duration, time_points):
+        initial_state = [initial_angle, 0]  # angle and angular velocity
+        t = np.linspace(0, duration, time_points)
+        solution = odeint(self.derivatives, initial_state, t)
+        return t, solution
+
+def main():
+    st.title("Simple Pendulum Simulator")
+    
+    # User inputs
+    length = st.slider("Pendulum Length (m)", 0.1, 5.0, 1.0)
+    initial_angle = st.slider("Initial Angle (degrees)", -90.0, 90.0, 45.0)
+    
+    # Convert to radians
+    initial_angle_rad = np.deg2rad(initial_angle)
+    
+    # Create and simulate pendulum
+    pendulum = Pendulum(length=length, gravity=9.81)
+    t, solution = pendulum.simulate(initial_angle_rad, duration=10, time_points=1000)
+    
+    # Plot results
+    fig, ax = plt.subplots()
+    ax.plot(t, np.rad2deg(solution[:, 0]))
+    ax.set_xlabel('Time (s)')
+    ax.set_ylabel('Angle (degrees)')
+    ax.grid(True)
+    st.pyplot(fig)
+    
+    # Display energy conservation
+    E_kinetic = 0.5 * length * solution[:, 1]**2
+    E_potential = 9.81 * length * (1 - np.cos(solution[:, 0]))
+    E_total = E_kinetic + E_potential
+    
+    st.write("### Energy Conservation")
+    st.line_chart({"Total Energy": E_total, 
+                   "Kinetic Energy": E_kinetic,
+                   "Potential Energy": E_potential})
+
+if __name__ == "__main__":
+    main()