All Questions
Tagged with classical-mechanics lagrangian-formalism
1,466
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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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Locally accessible dimensions of configuration space
I am reading a book called "Structure and Interpretation of Classical Mechanics"
by MIT Press.While discussing configuration space and degrees of freedom,the authors remark the following:
Strictly ...
CommunityBot
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Why the Lagrangian of a free particle cannot depend on the position or time, explicitly?
On p. 5 in $\S$3 pf the book of Mechanics by Landau & Lifshitz, it is claimed that
[...] for a free particle, the homogeneity of space and time implies
that Lagrangian cannot depend on ...
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Can classical Lagrangian mechanics be obtained directly from energy conservation?
Is there a way to derive classical Lagrangian mechanics (in particular, the classical Lagrangian $L = T-V$ and the Euler-Lagrange equation), under the simple assumption that mechanical energy is ...
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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:
$$ L = \frac{m}{2}(\dot{\rho}^2 + \rho^2\dot{\phi}^2) + ...
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How to calculate generalized force $Q_\phi$ with d'Alembert's principle?
The related post was found here Lagrangian formalism application on a particle falling system with air resistance and also Wikipedia's definition on generalized force. Essential
$$\frac{d}{dt}\frac{\...
CommunityBot
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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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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 ...
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What are the boundary conditions associated to this lagrangian?
Suppose that $L(q^i, \dot{q}^i)$ is a standard and well behaved lagrangian associated to some Dirichlet boundary conditions : $q^i(t_1) = q_1^i$ and $q^i(t_2) = q_2^i$. Now I have this new lagrangian ...
- 207k
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A particle constrained to always move on a surface whose equation is $\sigma (\textbf{r},t)=0$. Show that the particle energy is not conserved
In Goldstein's Classical mechanics question 2.22
Suppose a particle moves in space subject to a conservative potential $V(\textbf{r})$ but is constrained to always move on a surface whose equation is ...
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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 ...
- 207k
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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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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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