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2answers
53 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). ...
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1answer
52 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 ...
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1answer
79 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 ...
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1answer
224 views

Degrees of freedom in double Atwood machine?

Why the degree of freedom in double Atwood machine (one block on one side and a pulley with one block in its each side on other side) is 2 and not 1? According to the formula $s=3*n-m$; where $n=$...
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1answer
51 views

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 ...
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0answers
107 views

The consistency conditions of constrained Hamiltonian systems

I am studying the Hamiltonian description of a constrained system. There are some questions puzzled me for days, which I have been stuck on it. From the lagrangian, we can obtain the primary ...
3
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0answers
135 views

Lagrangian with vanishing conjugate momentum, independent variables

Given a Lagrangian density $\mathcal L(\phi_r,\partial_\mu\phi_r,\phi_n,\partial_\mu\phi_n)$, for which we find out that for some $\phi_n$ its conjugate momentum vanishes: $$\pi_n=\frac{\partial\...
3
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0answers
164 views

Do primary first class constraints change the electric field in the Hamiltonian form of Maxwell's theory?

In my understanding of Dirac's theory of constrained Hamiltonians, the primary (and also the secondary) first class constraints are generators of canonical transformations that do not change the ...
2
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0answers
98 views

Why do Lagrange multipliers work in mechanics?

I understand that it is not always simple to find generalized coordinates that satisfy the constraint equations, so we try to find an alternative (more mechanical) method that yields curves that ...
2
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0answers
214 views

Intuition behind the principle of virtual work

To derive Lagrange's Equations we need the principle of virtual work first. This principle states that whenever a system of $K$ particles is constrained to a submanifold $\mathcal{M}\subset \mathbb{R}^...
2
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0answers
55 views

A question about the constraints in BRST-Fock theories

In BRST Symmetry in the Classical and Quantum Theories of Gauge Systems, Henneaux says the Fock representation is not applicable to an odd number of constraints. Then he goes on to say that the Kugo-...
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0answers
56 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 ...
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0answers
35 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 ...
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0answers
35 views

When the equations of motion are not unique (eg. when they are given by eigenvectors), which will the free particle adhere to?

For this question I think it will be easier to express the usual equation describing the motion of a "free particle,"--viz. $g_{ij}\dot{x}^i\dot{x}^j$--in matrix form as follows: $$g_{ij}\dot{x}^i\...
1
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0answers
83 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 ...
1
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0answers
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 ...
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0answers
112 views

Calculation of the Poisson bracket of a (Classical) Yang-Mills generator

This question might be too technical or minute, but I believe someone can give me the right advise. What I want to calculate is a Poisson bracket algebra of classical YM gauge generators, \begin{...
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0answers
136 views

Restrained double pendulum

The equations of motion of a double pendulum are well-known. Usually you'd have the them expressed in the rotations $\theta_1(t)$ and $\theta_2(t)$. There are two degrees of freedom. Now consider the ...
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0answers
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 ...
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0answers
54 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 ...
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0answers
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 ...
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0answers
32 views

The Hamilton-Suslov principle

Building on the introduction given in the following paper, how does the Hamilton-Suslov principle generalise Hamilton's principle to consider contained mechanics? \begin{equation} \int ^{t_1}_{t_0}\...
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0answers
118 views

Question about an example of non-integrable constraints

The example is a thin disk rotating of an inclined plane. The disk can roll not only down the plane, but also "sideways". Let $(x,y)$ be the position of the CM, where the $y$ axis is down the slope ...
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0answers
93 views

Classical rod-wall-floor system

I have a homogeneous thin rod $AB$. $A$ can slide along $z$-axis, $B$ along $xy$ plane. There is no friction. We have any initial conditions. Now the question is to write down the equation of motion ...
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0answers
27 views

Classical mechanics: constraints

How to determine a constraint relation of a given system and identity whether the constraint is scleronomic or rheonomic, holonomic or non-holonomic, bilateral or unilateral just by looking at the ...