# Tagged Questions

The tag has no usage guidance.

40 views

### Work done by internal forces of a rigid body

I am reading Goldstein's Classical Mechanics book, and I came across that: In a rigid body the internal forces do no work Is this statement based on the assumption that the internal forces are ...
26 views

### In d'Alembert's principle, how that the Reverse effective force and Force of constraints are different?

In d'Alembert's principle, how that the Reverse effective force and Force of constraints are different? Both are opposition or restriction on the body but how both be different in real?
106 views

### Question on the constraint force of a string

I would like to know if the following statement is true or false even if I expect that it is true. Notation: I will consider a string that has no mass and that can not be extended. Saying that a ...
55 views

### Virtual Work- Is the presentation in Cornelius Lanczos wrong?

Book: The Variational Principles of Mechanics by Cornelius Lanczos Edition: 4th Chapter: 3, The Principle of Virtual Work I am on the second page of the 3rd chapter (pg 75; it has the Eqn. 31.1). ...
56 views

### Why does the 'Jacobian of at least one combination of $n$ functions shall be different from zero'?

I've started reading The Variational Principles of Mechanics by Cornelius Lanczos; here is the concerned excerpt from p. 11: The generalized coordinates $q_1,q_2,\ldots, q_n$ may or may not have a ...
53 views

### A pendulum attached to a spring and all the system is rotating with angular velocity

Find the all the constraints and a set of generalized coordinates A pendulum attached to a spring and all the system is rotating with angular velocity $\omega$. this is what I have done, I do not ...
12 views

### Computing the dynamics with a bilateral constraint in position

Let's says I have a dynamical system of generalized coordinates $x$, subject to a bilateral constraint $g(x(t),t)=x_1(t)-d(t)=0$ where $d$ is a prescribed displacement. I am looking for the ...
92 views

### Lagrange Multipliers and Virtual Work: Are Joos & Freeman wrong?

I have come to suspect that the treatment of virtual work in configuration space using Lagrange multipliers given here "Theoretical Physics, by Georg Joos & Ira M. Freeman, pg 114" is not correct. ...
100 views

### Hamilton's equations of motion on Dirac's formalism

I'm having several doubts about the procedure proposed by the Dirac-Bergmann algorithm in order to get the correct equations of motion of electrodynamics (Maxwell's equations). Suppose I've already ...
68 views

### Find the acceleration of the bead [closed]

Two identical, uniform large rings, each of mass $\text{m}$ are connected through a bead of same mass, which can move freely. When bead is released, it starts sliding down. The large rings roll over a ...
54 views

### Membrane Theory

I'm not a physicist or educated mathematician, so please excuse me if my question is scientifically rudimentary. It concerns Membrane Theory. If all open strings are attached to the surface of the D ...
57 views

### Non-null hessian condition for regular dynamical systems

I'm "researching" on unquantised Yang-Mills theory. For that I'm studying the Dirac's method for singular constrained systems and having problems to follow the first considerations on that matter. I ...
56 views

### Build rotational Hamiltonian based on Lagrangian of general form

I've been told that one could build rotational Hamiltonian based on Lagrangian of general form: $\mathcal{L} = \mathcal{L} (\vec{\Omega})$. By introducing Euler angles one could rewrite Lagrangian in ...
83 views

116 views

### Classical particle in a box [closed]

I'm trying to work out some of the details for this system. A particle with mass $\mu$, initial velocity $v_0$ at $x_0$ and moving freely between two walls located at $\pm L/2$, with which it bounces ...
36 views

### Finding the constraint equation

I am trying to solve a problem on Constraint equations for a triple pendulum model, but was not able to derive a constraint equation for the last mass. I solved constraint equations for Masses 1 ...
69 views

### How did he find the “lambda” value in this question? [closed]

There is a pdf i found when searching about Lagrangian Multpliers, but i was not able to understand how he derived lambda from two differential equations. If anyone can walk me through it, i would be ...
176 views

### People went down two different length slides end up at the bottom at the same time [closed]

Discussion I am having: If there are two slides that are at the same height. One slide is 100m long and the other slide is 200m long. The endpoint and start point are the same displacement. In ...
50 views

### Counting number of degrees of freedom in constrained system

Following Counting degrees of freedom in presence of constraints, we know that there would be N-2M-S dofs if we have M 1st-class constraints and S 2nd-class constraints in N-dim phase space. I don't ...
112 views

### Differential holonomic constraints

Differential holonomic constraint is an integrable homogeneous first order differential equation: $$\sum_{i}\mathcal{E}_{i}(q)\frac{dq_{i}}{d\tau}=0;$$ in which $\sum_{i}\mathcal{E}_{i}(q)dq_{i}$ is ...
35 views

55 views

### Relation between interaction Lagrangian and interaction Hamiltonian

I work with this interaction Lagrangian density $$\mathcal{L}_{int} = ia\bar{\Psi}\gamma^\mu\Psi Z_\mu +ib(\phi^\dagger\partial_\mu \phi - \partial_\mu\phi^\dagger \phi)Z^\mu,$$ where $Z^\mu$ is an ...
25 views

### A function of a constraint in a mechanics question not equaling zero?

Is this an error (I wrote what I think should be written), or is it okay that the constraint functions do not equal zero? I thought constraint functions are of the form $g(x,\dot {x},t)=0$, so in ...
106 views

### Problem in constraint equations

In this, if I want the acceleration constraint between $M$ and $2M$, I write $AM+2AB$=LENGTH OF STRING, which on differentiating twice gives $a_{m}=2a_{2m}$(which turns out to be correct). However, if ...
90 views

### Dirac bracket for a constrained particle

I am trying to work through a simple example of how to use the Dirac bracket from the following paper. In particular section 4 where the authors consider a constrained particle with the following ...
85 views

### Why don´t we just do a Legendre transform for a GR hamiltonian?

In general, if one has a well defined lagrangian for a field theory, which depends on a field, say $A_{\mu}$ and on its first spatial and temporal derivatives, we can simply define the canonical ...
26 views

### Is static gauge quantization of the particle equivalent to covariant quantization?

In the covariant quantization one is able to get directly (from the constraint $p^\mu_\mu+m^2=0$) the Klein-Gordon equation. But if one uses the parametrization $\tau=X^0$ then the Schrodinger ...
118 views

97 views

### Degrees of freedom of a point mass sliding on a rigid curved wire without friction

I am very new to the subject and am going through Structure and Interpretation of Classical Mechanics. One exercise asks to find the degrees of freedom of a number of systems, one of which is a ...
384 views

### Reduction of Nambu Goto action to true degrees of freedom

First consider the particle $$S=m\int\sqrt{-\dot{X}^2}d\tau$$ if you choose the static gauge $\tau=X^0$ and replace it in the action you get $$=m\int\sqrt{1-\dot{X}^j\dot{X}^j}d\tau$$ So now, you ...
227 views

### How to find the rank of the matrix $\frac{\partial ^2\mathcal{L}}{\partial \dot{X^\mu} \partial \dot{X^\nu} }$ for the Nambu-Goto string Lagrangian?

In this case $$\mathcal{L}~=~-T\sqrt{-\dot{X^2}X'^2+(\dot{X}\cdot X')^2}.$$ I was reading some books and papers about the constraints in the Nambu-Goto action, and all of them say something like ...
72 views

### Advantages of having a first class system and possibility of transforming a system into a first class one

I have two questions regarding first class systems. What are the advantages of having a first class Hamiltonian (a Hamiltonian whose all constraints are first class) in a theory or having a first ...
57 views

### Parabolic slide [closed]

Can you give a big hint for this problem please? A material point is released at the end of a track in the form of a vertical arc of parabola $y = x^2$ in $[-1,1]$, the meter is selected as a unit ...
230 views

### What is the position as a function of time for a mass falling down a cycloid curve?

In the brachistochrone problem and in the tautochrone problem it is easy to see that a cycloid is the curve that satisfies both problems. If we consider $x$ the horizontal axis and $y$ the vertical ...
85 views

For a particle trapped inside a rectangular box of side lengths $l_x$ $l_y$ and $l_z$, the energies are $E_{n_x,n_y,n_x}=\frac{\pi^2\hbar^2}{2m}(\frac{n_x^2}{l_x^2}+\frac{n_y^2}{l_y^2}+\frac{n_z^2}{... 2answers 285 views ### Non-relativistic QFT Lagrangian for fermions Take the ordinary Hamiltonian from non-relativistic quantum mechanics expressed in terms of the fermi fields$\psi(\mathbf{x})$and$\psi^\dagger(\mathbf{x})$(as derived, for example, by A. L. Fetter ... 1answer 134 views ### Hamiltonian field equations constraints Let's consider the Lagrangian $$\mathcal{L}~=~-\frac{1}{2}(\partial_\mu\phi^\nu)^2+\frac{1}{2}(\partial_\mu\phi^\mu)^2+\frac{1}{2}m^2\phi_\mu \phi^\mu,$$ with Minkowski metric$\eta_{\mu\nu}={\rm ...
In Polchinski's String theory book, Vol 1., in chapter 1, p. 18, he is deriving the Lagrangian in the light cone gauge (that's not necessary to know in order to answer this question), and he gets L~...
Poisson in Relativist's Toolkit and also other authors in various papers state explicitly that after one does the 3+1 decomposition, the lapse and shift $N$ and $N^a$ are non-dynamical variables, and ...