Linked Questions

2 votes
2 answers

Finding the value of the holonomic constraint forces

So let's say I have a Lagrangian augmented with some holonomic constraints. $$L' = L + \sum_i \lambda_i(t) f_i(q,t).\tag{i}$$ The solutions is the system of differential equations: $$\frac{\partial ...
azani's user avatar
  • 225
0 votes
1 answer

Goldstein Classical Mechanics equation 8.20 clarification

In Goldstein (Third Edition, Page 339) the equation 8.20 is as follow: $$ H = \dot q_ip_i - L = \dot q_ip_i-[L_0(q_i,t)+L_1(q_i,t)\dot q_k+L_2(q_i,t)\dot q_k\dot q_m].\tag{8.20}$$ Can someone ...
Cheng Tao's user avatar
  • 225
3 votes
1 answer

Lagrange multipliers $\lambda$ in Nonholonomic systems and Costates $\lambda$ in Optimal control theory

In Structure and Interpretation of Classical Mechanics, Section 1.10.3 by Sussman & Wisdom, talking about systems with non-holonomic constraints, it says the following about the Lagrange equations ...
Thomas Antony's user avatar
3 votes
1 answer

What does Thornton and Marion mean by "validity of Lagrange's equations"?

I am a bit confused about the 2nd statement below from Thornton and Marion 7.4: It is important to realize that the validity of Lagrange's equations requires the following two conditions: The forces ...
P'bD_KU7B2's user avatar
1 vote
1 answer

How do non-holonomic constraints work in Hamiltonian formalism?

In Lagrangian formalism, if $(M, g)$ is our configuration manifold, equipped with a Riemannian metric $g\in Hom(TM\bigotimes TM, \mathbb{R})$, Lagrangian function $\mathcal{L} : TM\times \mathbb{R}_{+}...
user avatar
2 votes
1 answer

Independence of generalized coordinates in the derivation of Lagrange equations from d'Alembert's Principle

I am confused by this remark in the derivation of Lagrange equations from d'Alembert's principle in Goldstein: I am not comfortable that I understand why, at this late stage of the derivation, they ...
heranias's user avatar
1 vote
1 answer

Solving this non-holonomic system using Dirac-Bergmann theory

I have read in some books and articles that the Dirac-Bergmann procedure to deal with constraints in phase space does not care about holonomic and Non-holonomic constraints, but I've been unable to ...
AndresB's user avatar
  • 426

15 30 50 per page