All Questions
Tagged with classical-mechanics lagrangian-formalism
251
questions with no upvoted or accepted answers
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Stationary solutions
I would like to know what stationary solutions means in this classical mechanics problem: On a vertical plane there is a rotating massless infinitely long rod with a fixed point $O$ on the plane. On ...
- 229
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791
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Generalized Coordinates in the Lagrangian Formalism -- What and How to Choose
Im having trouble figuring which generalized coordinates to choose; and even after having written down the Lagrangian of a system, which coordinates do I choose to write down the relevant Euler-...
- 705
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66
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Are time-$t$ maps of a Hamiltonian system with 1 degree of freedom typically twist?
If we take a typical Hamiltonian system $H(q,p)$ with one degree of freedom, and look at its time-$1$ map $(q(0),p(0)) \mapsto (q(t),p(t))$, will it generically satisfy the twist property, e.g. $\...
- 321
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Simple real life applications of Euler-Lagrange equations of motion
If you read some introductory mechanics text like David Morin's Introduction to Classical Mechanics about Euler Lagrange Equations you get a large amount of simple examples like the "moving plane" (...
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A bead is threaded on a frictionless vertical wire loop of radius R
The question is the very last sentence at the end of this post. In this post, I'll demonstrate how I reach to a contradiction(the conditions mentioned in conjecture 1 should be satisfied by all ...
- 219
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543
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Two Particles in a Harmonic Oscillator with repulsive short-range potential
Do bear with me, I am attempting to learn to write some simulations on the computer and learn some simple MD, so I defined sort of a toy problem.
I have two particles confined in a Harmonic Potential ...
- 425
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79
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What justification is necessary for convolutional variational principles to be considered legitimate?
I recently asked a related question and was interested in why/or why we cannot use convolutional variational principles in practice or in theory.
Summarizing the points I made in the earlier post:
...
- 411
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78
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Is there a straightforward simplified proof of energy conservation from time translation symmetry?
Electric charge conservation is easily proven from electric potential gauge symmetry, as follows:
The potential energy of an electric charge is proportional to the electric potential at its location.
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34
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What is the relationship between phase space and Jacobian in Nakahara Eq.1.15 (under this equation)?
In Nakahara's Geometry, topology and physics, under Eq.1.15 they give an equation
\begin{align*}
\det\left(\frac{\partial p_i}{\partial\dot{q}_j}\right)=\det\left(\frac{\partial^2L}{\partial\dot{q}_i\...
- 37
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620
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Conservation theorem for cyclic coordinates in the Lagrangian
Suppose $q_1,q_2,...,q_j,..,q_n$ are the generalized coordinates of a system.
$q_j$ is not there in the Lagrangian (it is cyclic).
Then $\frac{\partial L}{\partial\dot q_j}=constant$
In Goldstein, it ...
- 293
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Can we take any physical quantity as a generalized co-ordinate in Lagrangian function?
Lagrangian function is a function of generalized co-ordinates $q_1,q_2,....$ & possibly of time $t$.
i.e. $L=L(q_1,q_2,....;t)$
Consider a simple pendulum.
Can I take
$q_1$ = kinetic energy of ...
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