I see what you mean. If I rewrite it as ##L = \frac{1}{2}m_1(\dot{x_1}^2 + \dot{y_1}^2) + \frac{1}{2}m_2(\dot{x_2}^2 + \dot{y_2}^2) - (-m_1gy_1 - m_2gy_2 + \frac{1}{2}k(\sqrt{x^2-y^2} -l_0)^2)##
should it be correct then?
And if, when I rewrite it with ##\theta_1, \theta_2## this part is going...