- Do the same equations of motion imply the same Lagrangians?🔍
- Lagrangians giving the same equations of motion🔍
- Equivalence of two lagrangians🔍
- Different Lagrangians can lead to the same equations🔍
- What kind of Lagrangians can we have?🔍
- What's up with the hypothetical system with a Lagrangian equal to a ...🔍
- The Lagrangian Method🔍
- Euler–Lagrange equation🔍
Different Lagrangians can lead to the same equations
Do the same equations of motion imply the same Lagrangians?
So if two lagrangians L1 and L2 are such that L1−L2=dΦdt for some function Φ, then they lead to the same equations of motion. You can find a ...
Lagrangians giving the same equations of motion - Physics Forums
Yes, it is possible for two Lagrangians to give the same equations of motion but lead to different physical predictions. This can happen if ...
Equivalence of two lagrangians - Mathematics Stack Exchange
In this case ˜L and L give rise to the same set of Euler Lagrange equations. In your case it is easy to see that such a function F can be ...
Different Lagrangians can lead to the same equations | Chegg.com
Science · Physics · Physics questions and answers · Different Lagrangians can lead to the same equations of motion. In particular, when we add ...
What kind of Lagrangians can we have? - MathOverflow
Do we always have to compare them to the form of the equations we derived previously? For example, the Lagrangian formalism seems to be ...
9.3: Lagrangian - Physics LibreTexts
There is an unlimited range of equivalent standard Lagrangians that all lead to the same equations of motion and satisfy the requirements of the ...
What's up with the hypothetical system with a Lagrangian equal to a ...
L=k|v|. One can easily check that in the one dimensional case this leads to the Euler-Lagrange equation being 0. This statement has a subtlety: ...
The two methods produce the same equations. ... In an actual problem, we would solve this equation for y0, and then separate variables and integrate.
Euler–Lagrange equation - Wikipedia
In classical mechanics, it is equivalent to Newton's laws of motion; indeed, the Euler-Lagrange equations will produce the same equations as Newton's Laws.
What exactly is the motivation for the Lagrangian and which ... - Reddit
There is a Lagrangian version of Newtonian mechanics. In fact it is a good place to start learning about Lagrangians due to it's relative ...
Why does the Lagrangian equal T-V? - Science Meets Fiction
The trouble is that the Lagrangian is the kinetic energy minus the potential energy: L=T-V. And I and many other physics students would say, “ ...
The two conditions found can be linked one to one to the Euler-Lagrange equations of motion, making sure that third and fourth or- der terms ...
Lagrangian mechanics - Wikipedia
... can lead to different motions. Simple pendulum. Since the rod is rigid, the position of the bob is constrained according to the equation f(x, y) = 0, the ...
On non-standard Lagrangian equations - arXiv
equation lead to the same equation of motion. Thus we shall work with x ... Lagrangians can give rise to widely different. Hamiltonian systems such that ...
Classification of Lagrangians with given Euler-Lagrange equations
In a sense, all the Lagrangians giving the same Euler-Lagrange equations are exhausted by transformations of your type (b), ...
What would happen if the Lagrangian was V-T rather than T-V?
The main difference between the Lagrangian in classical mechanics and the potential energy in mechanics is the role they play. The Lagrangian is ...
I. Standard Lagrangians and their Role in Population Dynamics
As it is well-known, Lagrangians can be of different forms and yet they would give the same equation of motion [5,7]. In most cases, the ...
Lagrange Equation - an overview | ScienceDirect Topics
The Lagrangian function is the difference between the kinetic energy and the potential energy; L = KE − PE. The dot means a time derivative; q . k = d ...
problem 2 different lagrangians can lead to the same equations of ...
Problem 2: Different Lagrangians can lead to the same equations of motion. In particular, when we add to the Lagrangian the total time derivative of a function ...
Implementation of the Lagrangian formalism using Julia
Actually, it is possible to have derivatives of different variables in the same equation. ... will lead to both r and \sin\theta in the same ...