In monetary Stock-Flow Consistent (SEC) models, accounting identities reduce the number of behavioral functions to avoid an overdetermined system of equations. We relax this restriction using a differential-algebraic equation framework of constrained dynamics. Agents exert forces the variables according to their desire, for instance to gradually improve their utility. The parameter "economic power" corresponds to their ability to assert their interest. In analogy to Lagrangian mechanics, system constraints generate additional constraint forces that lead to unintended dynamics. We exemplify the procedure using a simple SEC model and reveal its implicit assumptions about power relations and agents' preferences.