Linked Questions

37 votes
6 answers
66k views

What are holonomic and non-holonomic constraints?

I was reading Herbert Goldstein's Classical Mechanics. Its first chapter explains holonomic and non-holonomic constraints, but I still don’t understand the underlying concept. Can anyone explain it to ...
Akash Shandilya's user avatar
25 votes
2 answers
2k views

Lagrangian Mechanics - Commutativity Rule $\frac{d}{dt}\delta q=\delta \frac{dq}{dt} $

I am reading about Lagrangian mechanics. At some point the difference between the temporal derivative of a variation and variation of the temporal derivative is discussed. The fact that the two are ...
user37155's user avatar
  • 281
9 votes
5 answers
1k views

Are constraint forces infinite?

A lot of authors claim that mechanical constraints are idealizations obtained by allowing enforcing forces to be infinite. But I either disagree or don't know what they mean. The only case where I ...
zetzar's user avatar
  • 91
9 votes
4 answers
3k views

Derivation of Lagrange Equations from Newton's Second Law for a Non-holonomic System of Particles

I am interested to write down a derivation of Lagrange equations from Newton's second law for a non-holonomic system of particles. Here, I mention my derivation where I am stuck right at the last step....
Hosein Rahnama's user avatar
9 votes
2 answers
757 views

Adding gauge fixing directly by hand is different from by Lagrange multiplier?

Why is adding gauge fixing directly different from doing so by Lagrange multiplier? For simplicity, we don't use field model. Direct method Consider a system $$L(x,\dot x,y,\dot y)=\frac{\dot x^2}{...
maplemaple's user avatar
  • 2,147
5 votes
2 answers
1k views

Why can we assume independent variables when using Lagrange multipliers in non-holonomic systems?

I'm studying from Goldstein's Classical Mechanics, 3rd edition. In section 2.4, he discusses non-holonomic systems. We assume that the constraints can be put in the form $$f_\alpha(q, \dot{q}, t) =0, ...
Javier's user avatar
  • 28.3k
3 votes
1 answer
2k views

What objective function is Lagrange's equation of the first kind based on?

In Lagrangian mechanics, Lagrange's equation of the first kind states that $$ \frac{\partial L}{\partial r_k} - \frac{d}{dt}\frac{\partial L}{\partial \dot{r_k}} + \sum_{i=1}^C \lambda_i \frac{\...
Jeppe's user avatar
  • 33
4 votes
1 answer
2k views

Can the Lagrange multiplier method be used with non-holonomic constraints?

The confusion for me comes from page 46 of Goldstein, where he says "However, it has been proven that no such varied path can be constructed unless [the differential equations of constraint] are ...
spencerhall01's user avatar
3 votes
1 answer
983 views

Lagrangian Mechanics: semi-holonomic constraints

By switching to a different set of coordinates, can you make problem with semi holonomic constraints into a problem with holonomic constraints? If so, then when can you do this? I wold like to know if ...
Vebjorn's user avatar
  • 169
5 votes
3 answers
2k views

Hamilton's principle and virtual work by constraint forces

I have a question about the following page 48 from the third edition of Goldstein's "Classical Mechanics". I do not understand how (2.34) shows that the virtual work done by forces of ...
mononono's user avatar
  • 340
2 votes
2 answers
796 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 ...
AlphaBaal's user avatar
  • 410
1 vote
2 answers
1k views

Lagrange equations for non-holonomic monogenic system

For monogenic and a special case of non-holonomic constraints where we have$$ \sum_{k} a_{l k} d q_{k}+a_{t t} d t=0 \tag{2-20} $$ we use lagrange multipliers and hamiltons principle to reach the ...
Kashmiri's user avatar
  • 1,270
3 votes
1 answer
907 views

Application of Lagrange Multipliers in action principle

In Goldstein's Classical Mechanics, he suggests the use of Lagrange Multipliers to introduce certain types of non-holonomic and holonomic contraints into our action. The method he suggests is to ...
DentPanic42's user avatar
2 votes
2 answers
464 views

Principle of virtual work for non-holonomic constraints

Goldstein (3rd ed. page 17) derives the principle of virtual work for systems subject to holonomic constraints. For a system in equilibrium, the force can be decomposed into applied and constraint ...
VB0904's user avatar
  • 23
3 votes
1 answer
399 views

Why is d'Alembert's principle not as applicable in physics as the principle of stationary action?

Any textbook in classical mechanics will tell you that there are two different routes one can follow to derive the Euler-Lagrange equations: Route 1: Write d'Alembert's principle in the form $\sum_{i=...
Don Al's user avatar
  • 1,092

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