Dynamics and control issues of multi-rotor platforms

This thesis deals with the analytic study of dynamics of Multi--Rotor Unmanned Aerial Vehicles. It is conceived to give a set of mathematical instruments apt to the theoretical study and design of these flying machines. The entire work is organized in analogy with classical academic texts about airplane flight dynamics. First, the non--linear equations of motion are defined and all the external actions are modeled, with particular attention to rotors aerodynamics. All the equations are provided in a form, and with personal expedients, to be directly exploitable in a simulation environment. This has requited an answer to questions like the trim of such mathematical systems. All the treatment is developed aiming at the description of different multi--rotor configurations. Then, the linearized equations of motion are derived. The computation of the stability and control derivatives of the linear model is carried out. The study of static and dynamic stability characteristics is, thus, addressed, showing the influence of the various geometric and aerodynamic parameters of the machine and in particular of the rotors. All the theoretic results are finally utilized in two interesting cases. One concerns the design of control systems for attitude stabilization. The linear model permits the tuning of linear controllers gains and the non--linear model allows the numerical testing. The other case is the study of the performances of an innovative configuration of quad--rotor aircraft. With the non--linear model the feasibility of maneuvers impossible for a traditional quad--rotor is assessed. The linear model is applied to the controllability analysis of such an aircraft in case of actuator block.

Essays in the Economics of the Family and Cultural Transmission

My research aims at identifying the role cultural-ethnic traits play in marriage choices and at uncovering the implications of marital sorting on consequent intra-household decisions. From different perspectives, this thesis focuses on intermarriages, within the Italian marriage market. In the first chapter, I explore the role of ethnic endogamy on marital instability. I document the existence of a positive differential in marital instability of interethnic marriages compared to homogeneous ones and I demonstrate that genetic and ethnolinguistic measures of cultural diversity are informative about the incidence of marital dissolution. The second chapter investigates a novel channel, which explains the differential in household stability and investments across family types: cultural socialization of children. I propose a marital matching model along cultural-ethnic lines, to study the process of family formation and intra-household decision making in a context where ethnic differences between spouses potentially matter both in terms of preferences and technologies for household production. The observed intermarriage, fertility, separation and socialization rates are in line with theoretical predictions and they are consistent with strong preferences of parents toward cultural socialization of children to their own ethnic identity. In the third chapter, I propose and estimate a marital matching model along ethnic lines. I argue that gains to intermarriage depend on both cultural preferences and legal status motives. Taking advantage of the exogenous EU enlargements to East European countries in 2004 and 2007, I show that gains to intermarriage of East European migrants significantly decrease in response to the acquisition of the legal status. The final chapter aims to understand whether judicial decisions respond to the ethnic identity of spouses and what incentives those judgments are guided, by looking at separation and divorce sentences. Studying the legal custody assignment of children, I document a significant differential interacting mothers’ ethnicities with the family type.