Tagged Questions

3
votes
3answers
124 views

Virtual differentials approach to Euler-Lagrange equation - necessary?

I'm currently teaching myself intermediate mechanics & am really struggling with the d'Alembert-based virtual differentials derivation for the Euler-Lagrange equation. The whole notion of, and ...
1
vote
1answer
153 views

What's the motivation behind the action principle? [closed]

What's the motivation behind the action principle? Why does the action principle lead to Newtonian law? If Newton's law of motion is more fundamental so why doesn't one derive Lagrangians and ...
0
votes
0answers
67 views

What are the details of this variational calculus solution?

This answer includes the problem: Suppose you have a 2-d bullet going very fast through a 2-d gas. The gas molecules reflects specularly off the bullet, making glancing collisions. What shape of ...
14
votes
4answers
457 views

Is the principle of least action a boundary value or initial condition problem?

Here is a question that's been bothering me since I was a sophomore in university, and should have probably asked before graduating: In analytic (Lagrangian) mechanics, the derivation of the ...
5
votes
2answers
129 views

What shape of track minimizes the time a ball takes between start and stop points of equal height?

I was at my son's high school "open house" and the physics teacher did a demo with two curtain rail tracks and two ball bearings. One track was straight and on a slight slope. The beginning and end ...
2
votes
2answers
207 views

What is the significance of action?

What is the physical interpretation of $$ \int_{t_1}^{t_2} (T -V) dt $$ where, $T$ is Kinetic Energy and $V$ is potential energy. How does it give trajectory?
5
votes
4answers
727 views

Why can't any term which is added to the Lagrangian be written as a total derivative (or divergence)?

All right, I know there must be an elementary proof of this, but I am not sure why I never came across it before. Adding a total time derivative to the Lagrangian (or a 4D divergence of some 4 ...
2
votes
2answers
198 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 ...
3
votes
2answers
274 views

What are some interesting calculus of variation problems? [closed]

That I could create as a classical mechanics class project? Other than the classical examples that we see in textbooks (catenary, brachistochrone, Fermat, etc..)
12
votes
6answers
2k views

Why the Principle of Least Action?

I'll be generous and say it might be reasonable to assume that nature would tend to minimize, or maybe even maximize, the integral over time of $T-V$. Okay, fine. You write down the action ...
2
votes
1answer
206 views

What variables does the action $S$ depend on?

Action is defined as, $$S ~=~ \int L(q, q', t) dt,$$ but my question is what variables does $S$ depend on? Is $S = S(q, t)$ or $S = S(q, q', t)$ where $q' := \frac{dq}{dt}$? In ...
2
votes
1answer
485 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 ...