We show that the solution of Cauchy problem for the classical ODE \(m \mathbf {y}''=\mathbf {f}\) can be obtained as the limit of minimizers of exponentially weighted convex variational integrals. This complements the known results about weighted inertia-energy approach to Lagrangian mechanics and hyperbolic equations.

中文翻译：

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牛顿第二定律作为变分问题的极限

我们表明，经典 ODE \(m \mathbf {y}''=\mathbf {f}\) 的柯西问题的解可以作为指数加权凸变分积分的最小值的极限来获得。这补充了有关拉格朗日力学和双曲线方程的加权惯性能量方法的已知结果。