拉格朗日约束与微分Thomas分解
Lagrangian Constraints and Differential Thomas Decomposition
摘要：
在本文中，我们将展示如何计算算法的代数独立的约束奇异力学和场论模型与多项式拉格朗日函数的全套。如果所考虑的模型作为一个整体不是奇异的，但有域的动态（场）变量，其拉格朗日变得奇异，那么我们的方法允许检测这样的域和计算相关的约束。在这样做时，我们假设一个模型的拉格朗日量是一个微分多项式，并应用微分托马斯分解算法的欧拉-拉格朗日方程。
英文摘要：
In this paper we show how to compute algorithmically the full set of algebraically independent constraints for singular mechanical and field-theoretical models with polynomial Lagrangians. If a model under consideration is not singular as a whole but has domains of dynamical (field) variables where its Lagrangian becomes singular, then our approach allows to detect such domains and compute the relevant constraints. In doing so, we assume that the Lagrangian of a model is a differential polynomial and apply the differential Thomas decomposition algorithm to the Euler-Lagrange equations.
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