经典变分问题的宇宙类比
Cosmic analogues of classic variational problems
摘要：
几个经典的一维问题的变分起源于非相对论粒子力学的解决方案是类似的空间均匀和各向同性的宇宙。它们被一个方程所支配，这个方程在形式上是一个适合宇宙流体的弗里德曼方程。这些问题被重新审视，并指出它们的宇宙类似物。有些对应于宇宙学的主要解决方案，而其他类似于奇异的宇宙与幻影流体和有限的未来奇点。
英文摘要：
Several classic one-dimensional problems of variational calculus originating in non-relativistic particle mechanics have solutions that are analogues of spatially homogeneous and isotropic universes. They are ruled by an equation which is formally a Friedmann equation for a suitable cosmic fluid. These problems are revisited and their cosmic analogues are pointed out. Some correspond to the main solutions of cosmology, while others are analogous to exotic cosmologies with phantom fluids and finite future singularities.
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。
