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From Lagrangian I got two primary constraint $\phi_i$ and $\phi$. And my Hamiltonian in presence of the constraints becomes- $$H_p=p\dot q-L+\lambda_i\phi_i+\lambda\phi$$ here the $\lambda_i$ and $\lambda$ are Lagrange undetermined multiplier. Now from $\dot \phi_i=[\phi_i,H_p]$ I got secondary constraint $\Sigma_k$ and from $\dot \phi=[\phi,H_p]$ I got another secondary constraint $\Sigma$ . To satisfy the consistency condition I calculated the $\dot \Sigma_k=[\Sigma_k,H_p]$ and $\dot\Sigma=[\Sigma,H_p]$. $$$$ From the relation I have $\dot \Sigma\approx0$. But the $\dot \Sigma_k$ gives the value of of $\lambda_i$. Now can anyone help me how can I further analyze the constraints in this case? Do I have to put the value of $\lambda_i$ in the equation of $H_p$ and calculate the commutation again? An example would be lovely.

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As I know, from the time consistency of $\Sigma_i$ you will not get another constraint. You have to substitute the Lagrange multiplier in the Hamiltonian by what you got. But I can not understand what you want to say by $\dot{\Sigma}=0$. If you mean 0=0, it is the end! But if it gives you an expression you have to continue and consider $\dot{\Sigma}=0$ as a new constraint. Check whether this new expression does not be a linear combination of other constraints. Generally It is not necessary to add secondary constraints to the complete Hamiltonian ($H_p$).

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