Constraints in Hamilton's equations

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Constraints in the Hamiltonian framework are inherently accounted for when formulating the Lagrangian, as they influence the choice of generalized coordinates, effectively reducing the degrees of freedom. While textbooks often focus on constraints within the Lagrangian context, the Hamiltonian approach also incorporates these constraints through Hamilton's principle, where the integral of the Lagrangian is made stationary. For non-holonomic constraints, the treatment may differ slightly, yet the fundamental concept remains consistent. The discussion seeks a method analogous to the Lagrangian approach, specifically regarding undetermined constants and the handling of constraint equations. Understanding these parallels can enhance the application of constraints within Hamiltonian mechanics.
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My question is about the constraints in Hamiltonian viewpoint. I mean, where the constraints are put into the Hamilton's equations. Constraints are usually studied in Lagrange's equations in textbooks (such as Jose and Goldstein). However, I couldn't find anything about constraints in Hamiltonian viewpoint.
Thanks in advance.
 
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When you are constructing L, you do it in terms of generalised co-ordinates, which are the least number of free co-ordinates. The constraints have already been taken into account when constructing L by eliminating some degrees of freedom. When you are using Hamilton’s principle, you are making integral Ldt stationary, and, so here too, the constraints have been taken into account.

For non-holonomic constraints, the treatment may be somewhat different, but the essence is the same.
 
Dear Shooting star,
Thanks for writing. But I'm looking for some techniqe jist similar to one we use in Lagrangian viewpoint as undetermined constants and the way we treat with constraint equations there.
 
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