All Questions
Tagged with classical-mechanics lagrangian-formalism
1,464
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On Landaus&Lifshitz's derivation of the lagrangian of a free particle [duplicate]
I'm reading the first pages of Landaus&Lifshitz's Mechanics tome. I'm looking for some clarification on the derivation of the Lagrange function for the mechanical system composed of a single free ...
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Subsequent motion (time evolution) of angled dipoles in electric field
Suppose we have a system of two dipoles, each with dipole moment $\mathbf{p}=2aq$ each aligned at angles $\theta$ and $-\theta$ with the horizontal. I’m thinking of an angle bracket shape, essentially....
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How did the boundary term vanish in deriving equation of motion from Lagrangian? [closed]
I was deriving the equation of motion from Lagrangian, by using the principle of least action. Usually, at this point in derivation,
$$\int dt \frac{\partial L}{\partial \dot{q}} \frac{\partial}{\...
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1
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Analogy of Euler-Lagrange-equation and Continuity equation
It seems to me that there is a link between the continuity equation
$$\nabla\rho u + \frac{\partial \rho}{\partial t} = 0$$
and the Euler-Lagrange equation for Lagrangian mechanics
$$\nabla_q L - \...
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Why can't we treat the Lagrangian as a function of the generalized positions and momenta and vary that? [duplicate]
Some background: In Lagrangian mechanics, to obtain the EL equations, one varies the action (I will be dropping the time dependence since I don't think it's relevant) $$S[q^i(t)] = \int dt \, L(q^i, \...
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Question about Problem $12$ in Chapter $11$ from Kibble & Berkshire's book
I write again the problem for convinience:
A rigid rod of length $2a$ is suspended by two light, inextensible strings of length $l$ joining its ends to supports also a distance $2a$ apart and level ...
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"Pseudo-Potential" for acceleration in the $x$ plane?
First Post!
My study group for classical mechanics using Taylor and Thornton and Marion and I found this problem while trying to study for our final. The set up has a particle in a tube that is ...
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Group theoretical approach to conservation laws in classical mechanics
I'm doing some major procrastination instead of studying for my exam, but I wanted to share my thought just to confirm if I'm right.
Suppose that the action, $S(\mathcal{L})$ forms the basis of a ...
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1
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What is the benefit of Hamiltonian formalism to promote ($q,\dot{q},t$) from Lagrangian to ($q,p,t$) despite getting the same EOM finally? [duplicate]
Hamiltonian formalism follows
$$H(q,p,t)=\sum_i\dot{q_i}p_i-L(q_i,\dot{q}_i,t) $$ and $$\dot{p}=-\frac{\partial H}{\partial q}, \dot{q}=\frac{\partial H}{\partial p} $$
but finally these will get the ...
- 311
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Precise Definition of Degrees of Freedom [duplicate]
I am taking Analytical Mechanics and while reading Goldstein's and LL something bothered me: can I say that a degree of freedom is an independent (generalized) coordinate?
What bothers me is that we ...
user400821
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Perturbation of central field potential
i`d like to consider system with Coulomb potential: $U = -\frac{\alpha}{r}$ and constant magnetic field.It is easy to write Lagrangian function:
$$ L = \frac{m}{2}(\dot{\rho}^2 + \rho^2\dot{\phi}^2) + ...
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5
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What is the point of knowing symmetries, conservation quantities of a system?
I think this kind of question has been asked, but i couldn’t find it.
Well i have already know things like symmetries, conserved quantities and Noether’s theorem, as well as their role in particle ...
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Why does a free theory's action have to be quadratic?
From my naive understanding of the symmetry principle, in inertial frames the space is uniform and homogeneous, so the action must not depend explicitly on coordinates (or fields). Thus the action ...
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What is the physical significance of this generalised potential?
Consider a generalised potential of the form $U=-f\vec{v}\cdot\vec{r}$ where $f$ is a constant. This potential should not contribute any internal forces between particles as
\begin{equation}
\vec{F}=-\...
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Something fishy with canonical momentum fixed at boundary in classical action
There's something fishy that I don't get clearly with the action principle of classical mechanics, and the endpoints that need to be fixed (boundary conditions). Please, take note that I'm not ...
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