As the theoretical foundation of Lagrangian mechanics, Euler–Lagrange equation sets are widely applied in building mathematical models of physical systems, especially in solving dynamics problems. However, their preconditions are often not fully satisfied in practice. Therefore, it is necessary to verify their applications. The purpose of the present work is to conduct such verification by establishing a formal theorem library of Lagrangian mechanics in HOL Light. For this purpose, some basic concepts such as functional variation and the necessary conditions for functional extreme are formalized. Then, the fundamental lemma of variational calculus is formally verified and some new constuctors and destructors are proposed. Finally, the Euler–Lagrange equation set is formalized. To validate the formalization, the formalization results are applied to verify the least resistance problem of gas flow. The present work not only lays a necessary and solid foundation for application involving Lagrangian mechanics but also extends the HOL Light theorem library.

中文翻译：

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HOL光中基于变分微积分的欧拉-拉格朗日方程组的形式化

作为拉格朗日力学的理论基础，欧拉-拉格朗日方程组被广泛应用于建立物理系统的数学模型，尤其是求解动力学问题。然而，它们的先决条件在实践中往往不能完全满足。因此，有必要验证它们的应用。目前工作的目的是通过在 HOL Light 中建立一个正式的拉格朗日力学定理库来进行这样的验证。为此，一些基本概念，如功能变异和功能极端的必要条件被形式化。然后，形式化验证了变分微积分的基本引理，并提出了一些新的构造函数和析构函数。最后，将欧拉-拉格朗日方程组形式化。为了验证形式化，形式化结果用于验证气流最小阻力问题。目前的工作不仅为涉及拉格朗日力学的应用奠定了必要和坚实的基础，而且还扩展了HOL Light定理库。