Let's say I have an objective function $F$ with state variables $A,B,C$ and relative equations of motion, I can create the current time Hamiltonian with $H_C = F\{A,B,C\}+\alpha * \dot A+\beta * \dot B + \gamma \dot C$, where $\alpha, \beta, \gamma$ are the 3 co-state variables (I'm omitting here the control variables).
But what if I also have a constraint that in each moment in time I must have something like $aA + bB + cC = k$ (where $a,b,c,k$ are fixed parameters) ? How do I set this constraint in the hamiltonian ?
Of course I could simply use only the $A,B$ variables, but then I still have an equation of motion for $C$ (in my application $A$, $B$ and $C$ are different land use areas).