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Results tagged with lagrangian-formalism
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user 257521
For questions involving the Lagrangian formulation of a dynamical system. Namely, the application of an action principle to a suitably chosen Lagrangian or Lagrangian Density in order to obtain the equations of motion of the system.
1
vote
1
answer
151
views
Transformations in classical field theory and configuration space
When transforming a field in classical field theory the transformation of the four-gradient of this field follows automatically. At least this is what i have learned in my lectures.
This circumstance …
- 2,236
3
votes
Are there physical systems for which Hamiltonian is not defined?
You can in fact calculate the Hamiltonian to your Lagrangian! But first
let us take a look at the Lagrangian proposed by OP.
What are the dynamics?
The EoM obtained by the EL-equations are
$$
\frac{d} …
- 2,236
0
votes
Accepted
$O(3)$ sigma model for lumps
You start with the Lagrangian
$$
\mathcal L = \frac 1 4 \partial_\mu\vec \phi \cdot \partial^\mu\vec \phi + \nu(1 - \vec \phi \cdot \vec \phi),
$$
where $\vec \phi = (\phi_1, \phi_2, \phi_3)^T$ is the …
- 2,236
5
votes
Lagrange Equations for Non-Inertial Frame of Reference
I will start of this answer by a "simpler" example. Lets consider a free particle.
The Lagrangian for a non-relativistic free particle
$$
\mathcal L = \frac{m}{2}\mathbf v^2
$$
where $m \in \mathbb R_ …
- 2,236
1
vote
1
answer
317
views
Notation of derivatives in field theory
Some textbooks write
$$
\frac{\delta F_{\mu\nu}}{\delta(\partial_\sigma A_\kappa)}
$$
which sort of implies the derivative of a functional. Some other textbooks write
$$
\frac{\partial F_{\mu\nu}}{\pa …
- 2,236
1
vote
1
answer
365
views
Calculating the Equations of motion for a scalar field
I am recently trying to get some understanding of Quantum Field Theory, therefore I am reading Quantum Field Theory and the Standard Model by M.D. Schwartz. The author takes for an example the followi …
- 2,236
0
votes
Inclined plane - constraint - equation of motion
The question was more or less answered in the comments, but since there is no posted answer I will post one.
As pointed out in the comments OPs velocity vector is wrong.
OP has chosen polar coordinate …
- 2,236
0
votes
How to find the equations of motion with a constraint?
To expand the commend of Valter Moretti, I would also use a set of coordinates which already satisfy the spatial constraints.
So I would start by parameterizing the position vector as
$$
\mathbf r(t) …
- 2,236
2
votes
Complex Scalar Field - Euler Lagrange equation
I guess your confusion is caused by the assumption that $\phi^*$ is strictly connected to $\phi$. The thing is that you want to describe a field of the form
\begin{align}
\phi = \phi_1 + i \phi_2.
\en …
- 2,236
3
votes
Using the Lagrangian to find the equations of motion for a ball on an arbitrary hill
The question is more or less answered by the comments, but since there is no answer posted yet I'll post my answer anyway.
OP asks how to find the equations of motion of a point mass $m$ confined to a …
- 2,236
0
votes
Accepted
Complete analysis of a point on a surface with Lagrangian
The Problem:
So OP is dealing with the following problem.
A point particle with mass $m$ is confined to the submanifold
$$\mathcal{M} := \{(x,y,z)\in\mathbb R^3\ |\ y^2 + z^2 = 1\} \subset \mathbb R ^ …
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0
votes
Cart Pole kinetic energy
Let us start with an example first.
Consider a pendulum with constantly accelerated support (instead of the support being a degree of freedom of the system).
The position of said pendulum can be param …
- 2,236
1
vote
Calculating the Generalized force with and without the lagrangian
You are mixing up concepts from d'Alemberts principle and Lagrangian mechanics. To show you what is wrong we will look at an example which is related to your problem, s.t. you can find out the solutio …
- 2,236
1
vote
3
answers
220
views
Lagrange formalism in field theory
I recently had a discussion with a friend of mine who is like me studying physics. And we might got used to a misconception about the Lagrange-Formalism in field theory. In common field theory books o …
- 2,236
0
votes
Perturbation of central field potential
Since you notation is not quite concise I will do some guesswork in order to understand the underlying problem. The basic setting is that of a test particle that moves in a central potential $V(r)$. I …
- 2,236