Abstract Fundamental concepts for variational integrals evaluated on the solutions of a system of ordinary differential equations are revised. The variations, stationarity, extremals and especially the Poincaré-Cartan differential forms are relieved of all additional structures and subject to the equivalences and symmetries in the widest possible sense. Theory of the classical Lagrange variational problem eventually appears in full generality. It is presented from the differential forms point of view and does not require any intricate geometry.

中文翻译：

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一维变分积分的 Poincaré-Cartan 形式

摘要 修正了对常微分方程组的解求值的变分积分的基本概念。变化、平稳性、极值，尤其是庞加莱-嘉当微分形式，从所有额外的结构中解脱出来，并服从最广泛意义上的等价性和对称性。经典拉格朗日变分问题的理论最终完全具有普遍性。它是从微分形式的角度呈现的，不需要任何复杂的几何形状。