All Questions
9
questions
1
vote
1
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225
views
Lagrangian of rotational degrees of freedom for a diatomic gas
I'm reading David Tong's lecture notes on statistical mechanics and in the Diatomic Gas section, the partition function is divided into translational, rotational, and vibrational. Still, for the ...
- 13
1
vote
0
answers
47
views
Semi new approach to analyzing mechanical systems
In attempt to Analyze mechanical systems we have base our entire set of theorems on one principle which is very similar to the principle of stationary action:
“ System always evolves in a way that it ...
1
vote
0
answers
60
views
Does the Legendre transformation describe two views on the same physical system or different physical systems?
In mechanics we perform the Legendre transform to go from the Lagrangian $L(q, \dot{q})$ to the Hamiltonian $H(q, p)$. This seems to be describing the same physical system. $L$ and $H$ both describe ...
- 131
2
votes
0
answers
44
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How are conjugate variables in mechanics and stat mech related to duality in convex optimization?
I recently studied duality in optimization where a primal optimization problem can be casted as a dual problem which provides meaningful lower bounds on the primal. There is also a notion of conjugate ...
- 131
0
votes
1
answer
164
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Derivation of Lagrangian in generalized coordinates
I am reading Mark Tuckerman's Statistical Mechanics and I am going through his derivation of the Lagrangian in generalized coordinates, using the mass metric tensor $G$.
He defines kinetic energy as
\...
- 697
1
vote
1
answer
163
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Free Fall Conservation of Momentum
So I looked at the invariance of the Lagrangian under the Gallilei Transformations.
So for the free fall we have the Lagrangian
$$L = \frac{m}{2}\dot{z}^2 -mgz$$
Then I applied the transformation
$$x\...
1
vote
0
answers
445
views
What is the physical interpretation of the action integral, without the stationary action principle?
I'm still wondering about the physical interpretation of the action integral of some mechanical system (classical theory here, to simplify things):
\begin{equation}\tag{1}
A = \int_{t_1}^{t_2} L(q, \, ...
- 7,592
3
votes
0
answers
276
views
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
67
votes
5
answers
8k
views
Is there a Lagrangian formulation of statistical mechanics?
In statistical mechanics, we usually think in terms of the Hamiltonian formalism. At a particular time $t$, the system is in a particular state, where "state" means the generalised coordinates and ...
- 34.3k