All Questions
Tagged with stability lagrangian-formalism
16 questions
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Motion around stable circular orbit
Hello I am to solve whether it is possible for body of mass $m$ to move around stable circular orbit in potentials: ${V_{1} = \large\frac{-|\kappa|}{r^5}}$ and ${V_{2} = \large\frac{-|\kappa|}{r^{\...
- 11
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Ghost detection at the level of equations of motion
My question is about how to detect ghostly degrees of freedom at the level of equations of motion. It is not clear for me how does this work. Let me explain with an example:
Consider the following ...
- 567
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How can I show that the action of a SHO is a saddle-point solution if $t_{f} - t_{0} > T/2$?
In this post and in this post, QMechanic claims that a simple harmonic oscillator with Dirichlet boundary conditions has saddle-point solutions if $t_{f} - t_{0} > T/2$ where $T$ is the ...
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What is the problem of higher-order time derivatives with causality?
I've heard that equations of motion with third- or higher-order time derivatives have problems with causality, but can't seem to find any proof or reasoning for this. Could anyone please help me? I ...
- 21
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How do you check the stability of a kink solution?
I am reading a nice introductory note by Hugo Laurell (http://uu.diva-portal.org/smash/get/diva2:935529/FULLTEXT01.pdf) but got confused on section 3.2.
He claims the stability of kink by expanding a ...
- 311
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Lagrange with Higher Derivatives (Ostrogradsky instability) [duplicate]
In class our teacher told us that, if a Lagrangian contain $\ddot{q_i}$ (i.e., $L(q_i, \dot{q_i}, \ddot{q_i}, t)$) the energy will be unbounded from below and it can take any lower values (in other ...
- 3,160
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Is action maximized for a system in stable equilibrium?
Others have asked in general about cases in which the action integral is not minimized, but my question is specific: Can we show that the conventional action integral is always maximized for a system ...
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Why doesn't the Lagrangian depend on higher-order derivatives of position?
This isn't a duplicate of already-answered questions, but rather a follow-up of this answer. The author presents a field-theoretical argument whereby a problematic run-away particle creation is ...
- 1,355
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What does the Ostrogradsky instability have to do with stability?
Ostrogradsky's instability theorem says that under some conditions, a system governed by a Lagrangian which depends on time derivatives beyond the first is "unstable". In the proof, one computes the ...
- 1,032
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Stability of Schwarzschild and Reissner-Nordstrom spacetimes
I am interested to know what is the best we can say about stability of Schwarzschild and Reissner-Nordstrom black holes.
I found some who study the behavior of perturbations that satisfy the ...
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What is the "special time dependence" that develops in an Ostrogradskian instability?
I've been reading papers that deal with Lagrangians containing second- and higher- order derivatives of field variables. In this paper in Section 3.1, I found this very interesting quote:
The ...
- 25k
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Equilibria and conserved quantities in a superposition of central potentials
I have a Lagrangian made up of a superposition of $k$ central repulsive potentials centered at $(a_k,b_k)$. Each potential is somewhat strange - they take the form $V(r)=-\ln\left(r\right)$. The whole ...
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How to understand $L_4$ and $L_5$ Lagrange points gravity balance? [duplicate]
It's relative easy to understand gravity balance of Lagrange points $L_1$, $L_2$ and $L_3$. But I am having a hard time to understand how a body would be "kind of" balanced out on Lagrange points $L_4$...
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Why can kink not tunnel to the vacuum, making it topologically stable?
Why can the kink
$$\phi(x)=v\tanh\left(\frac{x}{\xi}\right)$$
not tunnel into vacuum $+v$ or $-v$ (with spontaneous symmetry breaking in the vacuum)?
From the boundary condition, $\phi(x)\rightarrow \...
- 49
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687
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Why are L4 and L5 Lagrange points stable as points and not part of a circle? [duplicate]
I read this Phys.SE thread which is similar
Why are L4 and L5 lagrangian points stable?
but I did not want to necro that thread. It seems that most discussions of a three body problem are presented ...
- 1,729
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Confusion regarding the principle of least action in Landau & Lifshitz "The Classical Theory of Fields"
Edit: The previous title didn't really ask the same thing as the question (sorry about that), so I've changed it. To clarify, I understand that the action isn't always a minimum. My questions are in ...
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