Talk:Variational integrator

Order of the Integrator
From the article: since $$L_d\left( t_0, t_1, q_0, q_1 \right) = \int_{t_0}^{t_1} dt\, L(t,q(t),v(t)) + \mathcal{O}\left(t_1 - t_0\right)^3$$, our integrator will be second-order accurate. May someone explain how to derive the second order? I mean, how does one obtain the $$\mathcal{O}\left(t_1 - t_0\right)^3$$ term? The trapezoidal rule itself is only first order accurate.

--129.187.194.33 (talk) 12:24, 6 October 2016 (UTC)