Using the ode45 Function to Compute a Double Pendulum Model

Using the ode45 function to compute the double pendulum model yields highly accurate numerical results. This model allows us to observe the motion trajectories of both pendulums and their dynamic interactions. To gain deeper insights into the system's behavior, we can plot corresponding phase diagrams that visualize the pendulums' state variables (e.g., angles and angular velocities). For enhanced realism, parameters such as pendulum masses, lengths, and initial conditions can be adjusted programmatically to analyze their impact on the system's dynamics. The implementation typically involves defining a system of ordinary differential equations (ODEs) representing the pendulum dynamics, where ode45 numerically integrates these equations using a 4th/5th order Runge-Kutta method. Key MATLAB functions like animatedline or drawnow can be used for real-time animation, while quiver or streamlice functions help visualize phase portraits. This approach enables comprehensive analysis of the double pendulum's chaotic behavior and sensitivity to initial conditions.