python_car_leapfrong_integration_function.py

def simulate_car_leapfrog(dt, total_time):
    """Simulate car with Leapfrog integration"""
    time = 0
    position = 0
    
    # Initialize velocity at half-step back
    # Start with a half-step using Euler to bootstrap
    velocity_half = 0
    accel_init = acceleration_curve(0)
    velocity_half = accel_init * (dt / 2)
    
    times = [0]
    velocities = [0]  # Store full-step velocities for plotting
    positions = [0]
    
    while time < total_time:
        # Get acceleration at current position/velocity
        # Estimate full-step velocity for acceleration calculation
        velocity_full = velocity_half + acceleration_curve(velocity_half) * (dt / 2)
        accel = acceleration_curve(velocity_full)
        
        # Leapfrog: update velocity at half-step, then position
        velocity_half_new = velocity_half + accel * dt
        position += velocity_half_new * dt
        time += dt
        
        # Store full-step velocity for comparison (average of half-steps)
        velocity_full = (velocity_half + velocity_half_new) / 2
        
        times.append(time)
        velocities.append(velocity_full)
        positions.append(position)
        
        velocity_half = velocity_half_new
    
    return times, velocities, positions