# Questions tagged [constrained-dynamics]

A constraint is a condition on the variables of a dynamical problem that the variables (or the physical solution for them) must satisfy. Normally, it amounts to restrictions of such variables to a lower-dimensional hypersurface embedded in the higher-dimensional full space of (unconstrained) variables.

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### Vertical Disk rolling (Goldstein page 15 ) [closed]

Consider a disk rolling on the horizontal xy plane constrained to move so that the plane of the disk is always vertical. The coordinates used to describe the motion might be x,y coordinates of the ...
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### (Anti)commutation of ghosts and fermions

I would like to ask whether fermionic Grassmann fields in a gauge theory path integral (say in QCD) should be chosen to commute or anticommute with ghost and anti-ghost fields. The way most textbooks ...
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### Lagrangian mechanics - constraint forces & virtual work

The constraint forces have the dot product 0 ($\textbf C \cdot \textbf x=0$, where $\textbf C$ and $\textbf x$ are vectors, x being the virtual displacement. But the dot product is 0 if $\textbf C$ ...
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### What is the major difference between Dirac and BRST quantization of point particle?

I have derived the action for the bosonic point particle and now I want to quantize it but there are two formalism: one is Dirac and the other one is BRST. I want to know what is the major difference ...
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### Exact differential equations and holonomic constraints

I understand that if a constraint equation given on a differential form is exact, that means it is also holonomic since I can find a solution. But there are other types of differential equations, like ...
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### How to impose this constraint on two particles on General Relativity?

Let $(M,g)$ be spacetime and consider a system composed of two particles of masses $m_1$ and $m_2$ connected by a massless rod whose lenght varies in time. This constraint is quite easy to implement ...
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### Frictionless motion along a surface defined by a function

I have recently been learning Lagrangian Mechanics and wanted to apply it to a case I came up with in my head. Say you have a function f(x) that is always > 0. If a box or some solid particle was ...
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### Why are constraint forces assumed to be perpendicular?

In Taylor, it is assumed that the constraint forces are perpendicular to the constraint surface. I am kind of wondering what the justification for this is. Sure, if you mention typical constraint ...
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### Virtual displacements

From Goldstein's Classical Mechanics, A virtual displacement of a system refers to a change in the configuration of the system as the result of any arbitrary infinitesimal change of the coordinates ...
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### What are the properties of constraint forces? [closed]

I've just started studying mechanics. I need to find the properties of the constraint forces. I've gone through many books and also searched on internet but do not find any thing useful.
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### Atwood Machine - with pulley attached to one mass. What's the constraint?

2 problems here: What is the force pulling $m_2$ when $m_1$ falls? I can only think of tension. When $m_1$ does fall (maybe a height $H$), does $m_2$ move $H/2$ to the right? Since the other end of ...
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### Why can we not set each applied force equal to zero?

With reference to page 17 of "Classical Mechanics" by Goldstein, Safko and Poole, the small paragraph after eq. 1.43, $$\sum_i \mathbf{F}^{(a)}_i \cdot \delta \mathbf{r}_i ~=~ 0.\tag{1.43}$$ I do not ...
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### Are generalised coordinates truly independent?

Say we have a system with two generalised coordinates $x$ and $y$. When we solve the equations of motion we find $x=x(t)$ and $y=y(t)$. I can invert one of these solutions to find $t=t(y)$ and ...
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### Confused about the definition of holonomic constraints [duplicate]

I'm reading Goldstein's Classical Mechanics and he defines a constraint on particles having radii $\mathbf{r}_i$ to be holonomic if it can be written as $f(\mathbf{r}_1, \mathbf{r}_2, \dots , t) = 0$. ...
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### Does d'Alembert principle hold for non-conservative forces?

I know that D'Alembert's principle doesn't hold for sliding friction. But does it hold for any non-conservative force (other than sliding friction) or not? Could you give some examples of non-...
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### What is “irreversible displacement”?

In this Wiki page on D'Alembert Principle they say that "The principle does not apply for irreversible displacements, such as sliding friction, and more general specification of the irreversibility is ...
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### How to determine the equations of motion of a rigid body's center of mass from a constraint?

Picture a rigid square with one of its vertices attached to the end of a massless rigid rod whose other end is attached to a point fixed in space. The motion is restricted to the plane containing the ...