This application simulates the double pendulum without damping.

Buttons:

• Restarts the simulation.
• Accesses other initial conditions and system parameters.
• Enables or disables the trajectory of the red particle.

This simulation works based on the Lagrangian

$ \mathcal{L} = \dfrac{1}{2}( m_1+m_2 )L_1^2 \dot{\theta}_1^2 + \dfrac{1}{2}m_2 L_2^2 \dot{\theta}_2^ 2+ $ $ + m_2 L_1 L_2 \dot{\theta}_1 \dot{\theta}_2 \cos (\theta_1 - \theta_2) + $ $ + ( m_1+m_2 ) g L_1 \cos \theta_1 + m_2 g L_2 \cos \theta_2 $

The equations of motion are solved by the fourth order Runge-Kutta method.

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