One Hamiltonian formalism query - source is Goldstein's book

Click For Summary
SUMMARY

The discussion centers on the necessity of having no constraint equations among coordinates in the Hamiltonian formulation, as stated in the 3rd edition of Goldstein's "Classical Mechanics," page 335, section 8.1. The participants explore the differences between Hamiltonian and Lagrangian formulations, emphasizing that while the Lagrangian formulation accommodates constraint equations, the Hamiltonian formulation does not. They highlight that Legendre transformations can be applied to Lagrangian equations with constraints to derive Hamiltonian-type equations, thus bridging the two formulations.

PREREQUISITES
  • Understanding of Hamiltonian mechanics
  • Familiarity with Lagrangian mechanics
  • Knowledge of Legendre transformations
  • Basic concepts of constraint equations in classical mechanics
NEXT STEPS
  • Study the differences between Hamiltonian and Lagrangian mechanics
  • Learn about Legendre transformations in detail
  • Research examples of constraint equations in Lagrangian mechanics
  • Explore applications of Hamiltonian mechanics in modern physics
USEFUL FOR

Students of classical mechanics, physicists interested in theoretical mechanics, and educators teaching advanced mechanics concepts.

swapnilp
Messages
10
Reaction score
0
In 3rd edition of Goldstein's "Classical Mechanics" book, page 335, section 8.1, it is mentioned that :

In Hamiltonian formulation, there can be no constraint equations among the co-ordinates.

Why is this necessary ? Any simple example which will elaborate this fact ?

But in Lagrangian formulation, there can be constraint equations. Then why not in Hamiltonian formulation ?
 
Physics news on Phys.org
Actually you can make Legendre transformation for the Lagrange equations with constraints and obtain Hamiltonian-type equations with constraints. No problem
 
Last edited:

Similar threads

Classical Which books are good for Lagrangian/Hamiltonian formulations for continuum?
  • · Replies 12 ·
Replies
12
Views
3K
Looking for good books explaining Lagrangian and Hamiltonian Mechanics
  • · Replies 28 ·
Replies
28
Views
5K
Graduate Non holonomic constraints in classical mechanics textbook
  • · Replies 2 ·
Replies
2
Views
1K
Classical Are There Scientific Errors in Goldstein's Classical Mechanics?
  • · Replies 20 ·
Replies
20
Views
5K
Undergrad Proof that canonical transformation implies symplectic condition
  • · Replies 7 ·
Replies
7
Views
2K
Classical Good book for Lagrangian and Hamiltonian Mechanics
  • · Replies 20 ·
Replies
20
Views
10K
Undergrad Virtual displacement is not consistent with constraints
  • · Replies 3 ·
Replies
3
Views
2K
Classical Lagrangian and Hamiltonian Celestial Mechanics
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Difference between Hamiltonian and Lagrangian Mechanics
  • · Replies 20 ·
Replies
20
Views
10K
Classical Which classical mechanics book has better content?
  • · Replies 20 ·
Replies
20
Views
20K