论文标题
变化计算中的反问题：新的发展
The inverse problem in the calculus of variations: new developments
论文作者
论文摘要
我们处理了确定Lagrangians在$ n $ seconders订购普通微分方程的系统中的存在和独特性的问题。使用外部微分系统理论（EDS）提出了许多最近的定理。特别是，我们指出了如何以$ n = 2 $概括杰西·道格拉斯（Jesse Douglas）著名的解决方案。然后，我们在任意维度$ n $中检查一类新的解决方案，并在维度3中给出一些非平凡的示例
We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of $n$ second order ordinary differential equations. A number of recent theorems are presented, using exterior differential systems theory (EDS). In particular, we indicate how to generalise Jesse Douglas's famous solution for $n=2$. We then examine a new class of solutions in arbitrary dimension $n$ and give some non-trivial examples in dimension 3
