What is a Simple Example of a Functional and Lagrangian in Gravity?

  • Context: Graduate 
  • Thread starter Thread starter CFDFEAGURU
  • Start date Start date
  • Tags Tags
    Example Functional
Click For Summary
SUMMARY

This discussion focuses on the concept of functionals and Lagrangians in the context of gravity, specifically referencing Hartle's book "Gravity." A functional is defined as a mapping from a function to a number, exemplified by the action integral S, which is expressed as S = ∫ L(x, dx/dt) dt. The Lagrangian L serves as the integrand in this functional, and the discussion emphasizes the distinction between functionals and ordinary functions. The Euler-Lagrange equations are introduced as a method to find extremal paths that minimize the action functional.

PREREQUISITES
  • Understanding of basic calculus, particularly integrals and derivatives.
  • Familiarity with the concept of Lagrangian mechanics.
  • Knowledge of functional analysis, specifically the definition of functionals.
  • Basic principles of classical mechanics and action principles.
NEXT STEPS
  • Study the Euler-Lagrange equations in detail to understand their derivation and applications.
  • Explore the concept of action principles in classical mechanics and their implications.
  • Learn about the role of Lagrangians in different physical systems, including free particles and constrained systems.
  • Investigate advanced topics in functional analysis, focusing on mappings and transformations of functions.
USEFUL FOR

Students and researchers in physics, particularly those studying general relativity, classical mechanics, and mathematical physics. This discussion is beneficial for anyone looking to deepen their understanding of functionals and Lagrangians in theoretical frameworks.

  • #31


I got it now.

Thanks a lot for all of your help.

Matt
 
Physics news on Phys.org
  • #32


I recommend that you also try to derive the Euler-Lagrange equations using the method I described earlier. It would give you a deeper understanding of these things, and I also find it much easier to remember the derivation than the actual equation for some reason.
 

Similar threads

High School Does Relativity Impact Gravity's Influence on Fast-Moving Objects?
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Local phase invariance of complex scalar field in curved spacetime
  • · Replies 2 ·
Replies
2
Views
2K
High School Simple reasoning that the equivalence principle suggests curvature
  • · Replies 48 ·
2
Replies
48
Views
5K
Graduate Looking for linear frame dragging formula
  • · Replies 3 ·
Replies
3
Views
776
Undergrad Invariance of Diff. Line Elems. in Hartle's Gravity: Intro to GR
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Jefimenko's Theory of Gravitation: Continued Discussion
  • · Replies 5 ·
Replies
5
Views
2K
Reliability of LLM for generating examples in mathematics
  • · Replies 25 ·
Replies
25
Views
849
Lagrangian equations with other kinds of constraints
  • · Replies 2 ·
Replies
2
Views
2K
Graduate What Are Examples of Lagrangians in Various Disciplines?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate What is the Expression for the Waveform of an In-Spiralling Compact Binary?
  • · Replies 1 ·
Replies
1
Views
2K