An Introduction to Riemannian Geometry by Leonor Godinho & José Natário
Author:Leonor Godinho & José Natário
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham
We can look for the global minima (or maxima) of the action by considering curves on .
Definition 5.2
A variation of is a map (for some ) such that and the map given by is differentiable. The curve is said to be a critical point of the action if
for any variation of .
Notice that the global minima (or maxima) of must certainly be attained at critical points. However, a critical point is not necessarily a point of minimum (or maximum). It turns out that the critical points of the action are solutions of second-order ODEs.
Theorem 5.3
The curve is a critical point of the action determined by the Lagrangian if and only if it satisfies the Euler–Lagrange equations
Download
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.
Algebraic Geometry | Analytic Geometry |
Differential Geometry | Non-Euclidean Geometries |
Topology |
Weapons of Math Destruction by Cathy O'Neil(4269)
Factfulness: Ten Reasons We're Wrong About the World – and Why Things Are Better Than You Think by Hans Rosling(3512)
Factfulness_Ten Reasons We're Wrong About the World_and Why Things Are Better Than You Think by Hans Rosling(2448)
Descartes' Error by Antonio Damasio(2333)
A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra) by Barbara Oakley(2310)
TCP IP by Todd Lammle(2269)
Applied Predictive Modeling by Max Kuhn & Kjell Johnson(2086)
The Book of Numbers by Peter Bentley(2078)
The Tyranny of Metrics by Jerry Z. Muller(2071)
Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets by Nassim Nicholas Taleb(2068)
The Great Unknown by Marcus du Sautoy(1870)
Once Upon an Algorithm by Martin Erwig(1855)
Practical Guide To Principal Component Methods in R (Multivariate Analysis Book 2) by Alboukadel Kassambara(1830)
Linear Time-Invariant Systems, Behaviors and Modules by Ulrich Oberst & Martin Scheicher & Ingrid Scheicher(1810)
Lady Luck by Kristen Ashley(1804)
Easy Algebra Step-by-Step by Sandra Luna McCune(1798)
Police Exams Prep 2018-2019 by Kaplan Test Prep(1758)
All Things Reconsidered by Bill Thompson III(1756)
Secrets of Creation, Volume 1: The Mystery of the Prime Numbers by Watkins Matthew(1654)