any of several principles that find the physical trajectory of a system by minimizing or maximizing some value computed over the proposed path (for instance geometric optics can be reproduced by insisting on a minimum time principle).
8
votes
1answer
1k views
Explicit Variation of Gibbons-Hawking-York Boundary Term
Are there any references that present the explicit variation of the Hilbert-Einstein action plus the Hawking-Gibbons-York boundary term, and demonstrate the cancellation of the normal derivatives of ...
4
votes
3answers
602 views
Hanging chain in a planet's gravitational field
The curve for a chain hanging between two poles in a uniform gravitational field is known as the catenary.
Is there known an expression for the curve of a hanging chain on a planet of mass $M$ which ...
2
votes
1answer
164 views
Vanishing of field strength in gauged WZW model
Consider gWZW action $S_{gWZW}(g,A)=S_{WZW}(g)+S_{gauge}(g,A)$, where $S_{WZW}$ is usual WZW action being sum of sigma model and WZ terms for field $g$ taking values in group $G$ and $S_{gauge}=\int ...
5
votes
2answers
463 views
How does one formulate boundary conditions in a variational approach?
Many equations of motion can be derived from a variational principle. To take a simple example, the wave equation $h^{ij} \partial_i \partial_j u = 0$ (where $h^{ij}$ is the Minkowski metric ...
10
votes
2answers
607 views
Treatment of boundary terms when applying the variational principle
One of the main sources of subtlety in the AdS/CFT correspondence is the role played by boundary terms in the action. For example, for a scalar field in AdS there is range of masses just above the ...
2
votes
1answer
484 views
Does Action in Classical Mechanics have a Interpretation? [duplicate]
Possible Duplicate:
Hamilton's Principle
The Lagrangian formulation of Classical Mechanics seem to suggest strongly that "action" is more than a mathematical trick. I suspect strongly ...
4
votes
3answers
392 views
Understanding boundary conditions on slices of AdS5
This is a thing Iïve seen on many papers dealing with Warped Extra Dimensions, specifically on slices of AdS5. But the one where it appears more clearly is a lecture by Tony Gherghetta:
...
3
votes
3answers
1k views
Derivation of Maxwell's equations from field tensor lagrangian
I've started reading Peskin and Schroeder on my own time, and I'm a bit confused about how to obtain Maxwell's equations from the (source-free) lagrangian density $L = ...
3
votes
3answers
364 views
Type of stationary point in Hamilton's principle
In this question it is discussed why by Hamilton's principle the action integral must be stationary. Most examples deal with the case that the action integral is minimal: this makes sense - we all ...
15
votes
5answers
2k views
Why does calculus of variations work?
How does it make sense to vary the position and the velocity independently?
Edit:
Velocity is the derivative of position, so how can you treat them as independent variables? Doesn't every physics ...
22
votes
5answers
1k views
Hamilton's Principle
Hamilton's principle states that a dynamic system always follows a path such that its action integral is stationary (that is, maximum or minimum).
Why should the action integral be stationary? On ...
