The quantum version of the free fall problem is a topic often skipped in undergraduate mechanics courses, because its discussion usually requires wavepackets built on Airy functions—a difficult computation. Here, contrary, we show that can be nicely simplified both for single particle and general many-body systems by making use gauge transformation corresponds to change reference frame from lab...

This paper addresses the capturing control problem of a plug-and-play modularized drag-free spacecraft system, including two spherical proof masses, where performance constraints, collision risk, uncertain model parameters, unknown external disturbances, and limited communication are considered simultaneously. First, nonlinear relative dynamics masses with respect to is formulated for capture p...

The family of one-rule grid semi-Thue systems, introduced by Alfons Geser, is the family of one-rule semi-Thue systems such that there exists a letter c that occurs as often in the left-hand side as the right-hand side of the rewriting rule. We prove that for any one-rule grid semi-Thue system S, the set S(w) of all words obtainable from w using repeatedly the rewriting rule of S is a construct...

In the present article we study the Inverse Electrodynamics Model. This model is a gauge and parity invariant non-linear Electrodynamics theory, which respects the conformal invariance of standard Electrodynamics. This modified Electrodynamics model, when minimally coupled to General Relativity, is compatible with static and spherically symmetric Reissner-Nordström-like black-hole solutions. Ho...