For questions involving the Lagrangian formulation of a dynamical system. Namely, the application of an action principle to a suitably chosen Lagrangian or Lagrangian Density in order to obtain the equations of motion of the system.

learn more… | top users | synonyms (1)

6
votes
4answers
3k 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 = ...
1
vote
1answer
365 views

Lagrangian density of linear elastic solid

I need the general expression for the lagrangian density of a linear elastic solid. I haven't been able to find this anywhere. Thanks.
8
votes
1answer
3k views

The Euler-Lagrange equation in special relativity

How can I derive the Euler-Lagrange equations valid in the field of special relativity? Specifically, consider a scalar field.
3
votes
2answers
579 views

Is there a conserved quantity that enforces planar orbits in central force motion?

From what I remember, one of the first steps in finding the equations of motion for an orbiting body is to argue that the body's motion has to be restricted to a plane, because the central force has ...
2
votes
3answers
351 views

What is the definition of momentum when a mass distribution $\rho(r,t)$ is given?

This question is Edited after recieving comments. What is the definition of momentum when a mass distribution $\rho(r,t)$ is given? Assuming a particle as a point mass we know the definition of ...
2
votes
1answer
309 views

Distinguishing mechanical systems from general dynamical systems

[Remark: I admit that my first attempt on What makes a space a real space? was rather ill-posed and led to some confusion. Sorry for that, but please give me a second try. Part of the confusion arose ...
23
votes
6answers
3k 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 ...
5
votes
3answers
1k views

Constraint force on a rod

I really hope someone will take a quick look at the following, I would just love to better understand it... This exercise is from Arnold's "Mathematical Methods of Classical Mechanics", p. 97 in the ...
9
votes
9answers
4k views

Book about classical mechanics

I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical ...
25
votes
5answers
2k 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 ...