 for the brachistochrone problem, but do not mention the prior work of Carathéodory on this approach.In economics, the objective function in dynamic optimization problems often depends directly on time only through exponential discounting, such that it takes the form
where formula_79 is referred to as the instantaneous utility function, or felicity function.This allows a redefinition of the Hamiltonian as formula_80 where
which is referred to as the current value Hamiltonian, in contrast to the present value Hamiltonian formula_82 defined in the first section.