Spacecraft dynamics under the action of Y-dot magnetic control law

The paper investigates the dynamic behavior of a spacecraft when a single magnetic torque-rod is used for achieving a pure spin condition by means of the so-called Y-dot control law. Global asymptotic convergence to a pure spin condition is proven on analytical grounds when the dipole moment is proportional to the rate of variation of the component of the magnetic field along the desired spin axis. Convergence of the spin axis towards the orbit normal is then explained by estimating the average magnetic control torque over one orbit. The validity of the analytical results, based on some simplifying assumptions and approximations, is finally investigated by means of numerical simulation for a fully non-linear attitude dynamic model, featuring a tilted dipole model for Earth׳s magnetic field. The analysis aims to support, in the framework of a sound mathematical basis, the development of effective control laws in realistic mission scenarios. Results are presented and discussed for relevant test cases

Flexible Memory Networks

Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks having the maximal number of flexible memory patterns, given a constraint graph on the network's connectivity matrix. Modulo a mild topological condition, we find a close connection between maximally flexible networks and rank 1 matrices. The topological condition is H_1(X;Z)=0, where X is the clique complex associated to the network's constraint graph; this condition is generically satisfied for large random networks that are not overly sparse. In order to prove our main results, we develop some matrix-theoretic tools and present them in a self-contained section independent of the neuroscience context.Comment: Accepted to Bulletin of Mathematical Biology, 11 July 201