A One Hamiltonian formalism query - source is Goldstein's book

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