Linked Questions

76 votes
7 answers
75k views

What is the difference between Newtonian and Lagrangian mechanics in a nutshell?

What is Lagrangian mechanics, and what's the difference compared to Newtonian mechanics? I'm a mathematician/computer scientist, not a physicist, so I'm kind of looking for something like the ...
grautur's user avatar
  • 941
57 votes
7 answers
20k views

Why should an action integral be stationary? On what basis did Hamilton state this 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 ...
tsudot's user avatar
  • 971
44 votes
3 answers
5k views

How general is the Lagrangian quantization approach to field theory?

It is an usual practice that any quantum field theory starts with a suitable Lagrangian density. It has been proved enormously successful. I understand, it automatically ensures valuable symmetries of ...
user avatar
40 votes
7 answers
10k views

Is there a proof from the first principle that the Lagrangian $L = T - V$?

Is there a proof from the first principle that for the Lagrangian $L$, $$L = T\text{(kinetic energy)} - V\text{(potential energy)}$$ in classical mechanics? Assume that Cartesian coordinates are used. ...
Chin Yeh's user avatar
  • 741
29 votes
4 answers
5k views

How do I show that there exists variational/action principle for a given classical system?

We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's ...
Debangshu 's user avatar
17 votes
7 answers
11k views

Motivation for form $L = T - V$ of Lagrangian

This question (in Lagrangian mechanics) might be silly, but why is the Lagrangian $L$ defined as: $L = T - V$? I understand that the total mechanical energy of an isolated system is conserved, and ...
Frank's user avatar
  • 3,403
14 votes
3 answers
962 views

Justification of the Least Action Principle using conservation of information

In this Phys.SE question, one answer (by Ron Maimon) claims that one can make the assumption of a least action principle plausible using Liouville's Theorem as another starting point of the theory. ...
Quantumwhisp's user avatar
  • 6,713
12 votes
3 answers
23k views

Advantages of Lagrangian Mechanics over Newtonian Mechanics [closed]

Here, I'm going to pose a very serious list of doubts I have on Lagrangian Mechanics. Can we learn Lagrangian Mechanics without studying Newtonian Mechanics? Does Lagrangian help in solving problems ...
Das's user avatar
  • 305
10 votes
1 answer
560 views

Heuristic Motivation for Lagrangian Formalism

Does anyone know a good heuristic motivation for the Lagrangian Formalism? I think most physicist just accept at one point that it works and thats that. I think I understand the historic origin. ...
jak's user avatar
  • 9,907
9 votes
2 answers
1k views

Does Newtonian $F=ma$ imply the least action principle in mechanics?

I've learned that Newtonian mechanics and Lagrangian mechanics are equivalent, and Newtonian mechanics can be deduced from the least action principle. Could the least action principle $\min\int L(t,...
High GPA's user avatar
  • 417
8 votes
3 answers
1k views

Is it circular reasoning to derive Newton's laws from action minimization?

Usually, a typical example of the use of the action principle that I've read a lot is the derivation of Newton's equation (generalized to coordinate $q(t)$). However, in the classical mechanics ...
Néstor's user avatar
  • 430
7 votes
1 answer
310 views

Why are action principles so powerful and widely applicable? [duplicate]

I've been trying to wrap my head around Lagrangian mechanics and Lagrangians in general, and I've found it difficult. After some thinking, I believe that the issue I have is with action principles. ...
user6873235's user avatar
6 votes
4 answers
6k views

Can you explain Fermat's Principle to me?

The textbook(F.A.Jenkins and H.E.White Fundamentals of Optics) states that the Fermat's principle is that the path taken by a light ray in going from one point to another through any set of media ...
Wang Yun's user avatar
  • 529
6 votes
3 answers
1k views

Principle of Least Action via Finite-Difference Method

I am reading Gelfand's Calculus of Variations & mathematically everything makes sense to me, it makes perfect sense to me to set up the mathematics of extremization of functionals & show that ...
bolbteppa's user avatar
  • 4,031
6 votes
1 answer
1k views

Least Action Principle (Classical and Quantum Theory)

I) My first question would be "why should classical systems obey the principle of least action ?" When we find out the propagator in quantum physics, we find the amplitude to be equal to the sum over ...
Jon Snow's user avatar
  • 575

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