Cosmic Analogues of Classic Variational Problems
Abstract
:1. Introduction
2. Geodesics of the Euclidean Plane and a Not-So-Trivial Analogue
3. The Catenary Problem
4. Minimal Surface of Revolution and Its Analogue
4.1. Dependent Variable
4.2. Dependent Variable
5. Cosmic Analogue of the Brachistochrone Problem
6. Geodesics of the Poincaré Half-Plane
7. The Gravity Tunnel
8. The Terrestrial Brachistochrone
9. Discussion and Conclusions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Instability of the Static Universe Analogous to the Terrestrial Brachistochrone
References
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Variational Problem | Lagrangian | Cosmic Analogue |
---|---|---|
Geodesics of | ||
Milne universe | ||
Catenary problem | ||
Minimal surface of revolution | same as above | |
no cosmic analogue | ||
Brachistochrone | , dust | |
cycloid | ||
Geodesics of Poincaré plane | , radiation | |
Terrestrial tunnel | ||
anti-de Sitter space | ||
Terrestrial brachistochrone | ||
hypocycloid |
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Faraoni, V. Cosmic Analogues of Classic Variational Problems. Universe 2020, 6, 71. https://doi.org/10.3390/universe6060071
Faraoni V. Cosmic Analogues of Classic Variational Problems. Universe. 2020; 6(6):71. https://doi.org/10.3390/universe6060071
Chicago/Turabian StyleFaraoni, Valerio. 2020. "Cosmic Analogues of Classic Variational Problems" Universe 6, no. 6: 71. https://doi.org/10.3390/universe6060071