Bağlı sarkaçlar

$$\mathcal{L}=\dfrac{1}{2}(m+m_1+m_2)L_1^2\dot{\theta}^2+\dfrac{1}{2}m_1L_2^2\dot{\theta}_1^2$$ $$+m_1L_1L_2\dot{\theta}\dot{\theta}_1\cos(\theta-\theta_1)+\dfrac{1}{2}m_2L_2^2\dot{\theta}_2^2$$ $$+m_2L_1L_2\dot{\theta}\dot{\theta}_2\cos(\theta-\theta_2)$$ $$+(m+m_1+m_2)gL_1\cos\theta+m_1gL_2\cos\theta_1+m_2gL_2\cos\theta_2.$$