  We investigate variational principles for the approximation of quantum
dynamics that apply for approximation manifolds that do not have complex linear
tangent spaces. The first one, dating back to McLachlan (1964) minimizes the
residuum of the time-dependent Schr\"odinger equation, while the second one,
originating from the lecture notes of Kramer--Saraceno (1981), imposes the
stationarity of an action functional. We characterize both principles in terms
of metric and a symplectic orthogonality conditions, consider their
conservation properties, and derive an elementary a-posteriori error estimate.
As an application, we revisit the time-dependent Hartree approximation and
frozen Gaussian wave packets.
