Linked Questions
13 questions linked to/from What does a Lagrangian of the form $L=m^2\dot x^4 +U(x)\dot x^2 -W(x)$ represent?
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Doubt in the expression of Lagrangian of a system [duplicate]
There is a problem given in Goldstein's Classical Mechanics Chapter-1 as
20. A particle of mass $\,m\,$ moves in one dimension such that it has the Lagrangian
\begin{equation}
L\boldsymbol{=}\...
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Can these different Lagrangians lead to the same equation of motions? [duplicate]
A particle of mass $m$ moves in one-dimension with position $x$ and potential $V(x)$, described by the Lagrangian $$ L = \frac{1}{12}m^2 \dot{x}^4 + m \dot{x}^2 V - V^2 $$ Show that the resulting ...
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What are examples of Lagrangians that not of the form $T-U$?
My Physics teacher was reluctant to define Lagrangian as Kinetic Energy minus Potential Energy because he said that there were cases where a system's Lagrangian did not take this form. Are you are ...
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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. ...
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Non-uniqueness of the Lagrangian
Goldstein, 3rd ed
$$
\frac{d}{d t}\left(\frac{\partial L}{\partial \dot{q}_{j}}\right)-\frac{\partial L}{\partial q_{j}}=0\tag{1.57}
$$
expressions referred to as "Lagrange's equations."
...
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Lagrangian of a relativistic free massive particle
Lagrangian for a relativistic free particle can be written as
$$L=-m_0c^2\sqrt{1-\frac{v^2}{c^2}} .\tag{1}$$
It gives correct expression of Hamiltonian which is
$$H=\sqrt{p^2 c^2+m_0^2c^4}.\tag{2}$$
...
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Do the same equations of motion imply the same Lagrangians? [duplicate]
If two Lagrangian (densities) $\mathcal{L}$ give the same equations of motion, are they equivalent?
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3
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How to think of Lagrangians? [duplicate]
I am struggling to come up with the "right" way to think of Lagrangians. For example, in Hamiltonian mechanics the Hamiltonian is simply the total energy of the system. In classical ...
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answer
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Damped harmonic Oscillator Lagrangian equivalence
The objective is to prove that the Lagrangian:
$$L'=\frac{2\dot x+\lambda x}{2\Omega x}\tan^{-1}(\frac{2\dot x+\lambda x}{2\Omega x})-\frac{1}{2}\ln(\dot x^2+\lambda \dot{x } x + \omega^2x^2), \qquad \...
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Can Lagrangians be not related to energy?
I understand that in Lagrangian mechanics, a Lagrangian can be written as $L=T-V$ where $T$ and $V$ are the kinetic and potential energy of the system, respectively. However, in this paper, it ...
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Is it always the case that the square root of a lagrangian gives the same equations of motion as the lagrangian itself?
Inspired by the Phys.SE post Geodesic Equation from variation: Is the squared lagrangian equivalent? I was wondering if it is always the case that the square root of a lagrangian gives the same ...
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Question from Classical mechanics Goldstein H [closed]
When we are given a Lagrangian as $L \equiv L(\dot{x}, V)$ where $V=V(x)$, while differentiating why do we set $\frac{dV}{d\dot{x}} = 0$?
Is it just because $V$ is a function of only $x$? Since it’s ...
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What is the physical interpretation of a Lagrangian with $\dot{x}^4$?
Among the exercises in the first chapter of Goldstein's book "Classical Mechanics", it appears the lagrangian
$$
L\left(x,\frac{dx}{dt}\right) = \frac{m^2}{12}\left(\frac{dx}{dt}\right)^4 + m\left(\...
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