The variational utility of a deterministic, infinite horizon consumption path is defined as the minimum value of an additive criterion, taken over all possible future values of the rate of time preference. Special cases of variational utility include additive and recursive models. A reduced-form capital accumulation problem under variational utility is studied here. The optimal capital path is characterized by a Hamiltonian dynamical system, together with two transversality conditions at infinity. The Hamiltonian structure is applied to standard additive, or recursive, capital accumulation problems. Under a separability assumption, a stability result is extended from the additive to the recursive case