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Answer by Qmechanic for Hamiltonian from a Lagrangian with constraints?
Comments to the question (v2):To go from the Lagrangian to the Hamiltonian formalism, one should perform a (possible singular) Legendre transformation. Traditionally this is done via the Dirac-Bergmann...
View ArticleAnswer by image357 for Hamiltonian from a Lagrangian with constraints?
The Hamiltonian is defined by$$ H = \sum_{i=1}^n \left( \frac{\partial L}{\partial \dot q_i} \dot q_i \right) - L $$So in your case: $ H' = H - \lambda f $
View ArticleHamiltonian from a Lagrangian with constraints?
Let's say I have the Lagrangian:$$L=T-V.$$Along with the constraint that $$f\equiv f(\vec q,t)=0.$$ We can then write:$$L'=T-V+\lambda f. $$What is my Hamiltonian now? Is it$$H'=\dot q_i p_i -L'~?$$Or...
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