Linked Questions

4
votes
2answers
742 views

Confusion with Virtual Displacement

I have just been introduced to the notion of virtual displacement and I am quite confused. My professor simply defined a virtual displacement as an infinitesimal displacement that occurs ...
5
votes
2answers
666 views

Why is this a non-holonomic constraint?

Wikipedia states: holonomic constraints are relations between the position variables (and possibly time1) which can be expressed in the following form: $$f(q_{1},q_{2},q_{3},\ldots ,q_{n},t)=0$$ ...
6
votes
4answers
414 views

Question about holonomic constraints

Goldstein says that when a system of $N$ particles is subject to $k$ holonomic constraints, the positions $\mathbf{r}_1, \dots, \mathbf{r}_N$ can be parameterized by $3N - k$ independent coordinates $...
4
votes
1answer
431 views

Holonomic constraints and degrees of freedom

Wikipedia and other sources define holonomic constraints as a function $$ f(\vec{r}_1, \ldots, \vec{r}_N, t) \equiv 0, $$ and says the number of degrees of freedom in a system is reduced by the ...
2
votes
2answers
139 views

Commutation relations inconsistent with constraints

In section $9.5$ of Weinberg's Lectures on Quantum Mechanics, he uses an example to explain the clasification of constraints. The Lagrangian for a non-relativistic particle that is constrained to ...
3
votes
2answers
212 views

Is every constraint involving only two coordinates integrable?

There is a footnote on Goldstein's Classical Mechanics (3rd ed., page 15) which says the following: In principle, an integrating factor can always be found for a first-order differential equation ...
2
votes
2answers
263 views

Conversion of non-holonomic constraints to holonomic

In the case of a disc rolling without slipping, we have a constraint $\dot{x}=a\dot{\theta}$ where $a$ is the radius of the disc. Note that I have considered $x$ and $\theta$ as the generalized ...
0
votes
1answer
204 views

Confusion about virtual displacement

From Goldstein: A virtual (infinitesimal) 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 $\...
2
votes
2answers
94 views

Is there any restriction on the Lagrangian of a system?

I have learned the calculus of variations in my previous semester, and now we are studying classical mechanics. What I found is that there is lots of lack of rigor in Lagrangian mechanics in ...
2
votes
1answer
112 views

Identify a Hamiltonian system consistent or not?

I'm sorry if my question is too classic and basic. As Dirac-Bergmann algorithm for Hamiltonian formalism, I find out that a Hamiltonian system is inconsistent if Poisson bracket of primary constraints ...