One Hamiltonian formalism query - source is Goldstein's book

[swapnilp]

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 ?

 

[zwierz]

Actually you can make Legendre transformation for the Lagrange equations with constraints and obtain Hamiltonian-type equations with constraints. No problem