关于曲线的全局不变欧拉-拉格朗日方程
On globally invariant Euler--Lagrange equations for curves
AI总结：
本文研究了曲线在欧几里得平面和空间中基于运动群的不变欧拉-拉格朗日方程，并扩展到四维闵可夫斯基时空，探讨了全局代数微分不变量及其与射影和共形群的关系。
摘要：
不变拉格朗日量会产生不变的欧拉-拉格朗日方程，文献中讨论了如何使用各种局部方法来计算这些方程。本文的重点是全局代数微分不变量。在这种情况下，计算可以以几种方面进行修改。我们将讨论与先前方法的关系以及一些基础方面。理论中将不变的欧拉-拉格朗日方程应用于欧几里得平面和空间中的曲线。我们扩展这些计算到下一个维度四（闵可夫斯基时空），这已经表现出计算挑战。我们还提供了其他示例的公式，即射影和共形（莫比乌斯）群，并与一些最近的应用相关联。
英文摘要：
Invariant Lagrangians yield invariant Euler-Lagrange equations, and it was discussed in the literature how to compute those using various local methods. The focus of this paper is on global algebraic differential invariants. In this case the computation can be modified in several aspects. We will discuss relations with previous approaches and some foundational aspects. The theory of invariant Euler-Lagrange equations was applied to curves with respect to the motion group in the Euclidean plane and space. We expand those computations to the next dimension four (Minkowski spacetime), which already exhibits computational challenges. We also provide formulas for other examples, namely the projective and conformal (Möbius) groups and relate to some recent applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
