  The aim of this paper is to present a novel physics-based framework for the
identification of dynamical systems, in which the physical and structural
insights are reflected directly into a backpropagation-based learning
algorithm. The main result is a method to compute in closed form the gradient
of a multi-step loss function, while enforcing physical properties and
constraints. The derived algorithm has been exploited to identify the unknown
inertia matrix of a space debris, and the results show the reliability of the
method in capturing the physical adherence of the estimated parameters.
