All Questions
Tagged with classical-mechanics lagrangian-formalism
251
questions with no upvoted or accepted answers
3
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answers
138
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Particle in "external potential" VS particle on "curved surface": equivalence?
Let's consider a non-relativistic particle - its position is $x(t)\in \mathbb{R}^n$ - in an external potential $\phi$, with Lagrangian $$L=\dot{x}^i \eta_{ij}\dot{x}^j/2 - \phi(x),\tag{1}$$
where $\...
- 5,078
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121
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Intuitive explanation on why velocity = 0 for a inverted pendulum on a wheel system
I believe I have solved below problem. I am not looking for help on problem-solving per se. I am just looking for an intuitive explanation.
Problem statement: wheel mass = $m_1$, even mass rod BC mass ...
- 131
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77
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Is there a unique accepted Lagrangian formulation of Nambu mechanics?
In section 5 of their 2000 paper "Nambu Mechanics in the Lagrangian Formalism", Ogawa & Sagae critique previous attempts by Bayen & Flato and by Takhtajan to formulate the theory ...
- 3,684
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122
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Physical interpretation of the definition of angular momentum in classical mechanics
To what I understand, the following is a valid way to introduce the angular momentum $\mathbf L$ in the Lagrangian system of a rigid body. We can consider the extended configuration space to be $M\...
3
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396
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Are all canonical transformations either a point transformation, gauge transformation or a combination of them?
It's regularly argued that in the Hamiltonian formalism, we have more freedom to choose our coordinates and that this is arguably its most important advantage.
To quote from two popular textbooks:
[S]...
- 10.1k
3
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answers
830
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Gauge freedom in Lagrangian corresponds to canonical transformation of Hamiltonian
I want to show that the gauge transformation
$$L(q,\dot{q},t)\mapsto L^\prime(q,\dot{q},t):=L(q,\dot{q},t)+\frac{d}{dt}f(q, t)$$
corresponds to a canonical transformation of the Hamiltonian $H(p, q, ...
- 1,187
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answers
141
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Relativistic configuration space in classical mechanics
Okay so a couple of questions. Firstly I realise that in order to study the dynamics of one particle (classically), we define the Lagrangian and Hamiltonian to be the maps from the tangent and ...
- 504
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276
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Lagrangian formulation of a themodynamics problem
I was wondering whether it is possible to derive the model of a thermodynamical system by combining thermodynamic equations and Lagrangian mechanics.
Let's consider the following closed system.
A ...
- 43
3
votes
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answers
714
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Non-canonical transformation
I would like to know any method to transform a known non-canonical set of variables to a canonical set for a given system. The Lagrangian and Hamiltonian are known in the non-canonical variables. I ...
- 81
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222
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Does the additivity property of Integrals of motion and Lagrangians valid in all situations?
I would like to know if the additivity property of an integral (constant) of motion valid in all situations ? It works for energy but does it work for all other integrals of motion in all kinds of ...
- 345
3
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606
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A question on Lagrangian dynamics an the velocity phase space
I've struggled in the past with understanding why we can treat position and velocity as independent variables in the Lagrangian, but I think I may have finally become a bit more enlightened on the ...
- 3,063
3
votes
2
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243
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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 ...
- 1,487
2
votes
0
answers
37
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Physical model described by modify Helmholtz equation
The wave equation $\partial_t^2u=c\Delta u$ is usually handled through a time-harmonic ansatz, which reduces it to Helmholtz equation $\Delta u+\omega^2u=0$.
I'm interested in the following modified ...
- 121
2
votes
1
answer
122
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Independence of generalized coordinates in the derivation of Lagrange equations from d'Alembert's Principle
I am confused by this remark in the derivation of Lagrange equations from d'Alembert's principle in Goldstein:
I am not comfortable that I understand why, at this late stage of the derivation, they ...
- 31
2
votes
1
answer
72
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Some doubts about action symmetry
We know that Symmetry of the Lagrangian ($\delta L = 0$) always yields some conservation law.
Now, if $\delta L \neq 0$, that doesn't mean we won't have conservation law, because if we can show action ...
- 525