Study of invariant solutions in a 4D map aiming to learn tools for applications in Astronautics

• Grant number: 18/25001-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2019
• End date: February 28, 2022
• Field of knowledge: Engineering - Aerospace Engineering - Flight Dynamics
• Principal Investigator: Priscilla Andressa de Sousa Silva
• Grantee: Henrique Figueiredo Cherulli
• Host Institution: Universidade Estadual Paulista (UNESP). Campus Experimental São João da Boa Vista. São João da Boa Vista , SP, Brazil

Abstract

Nonlinear dynamical systems model a variety of natural phenomena and engineering problems, ranging from mechanical rotors to interplanetary transfer trajectories. The elements that allow practical applications of such diverse systems are the invariant solutions of chaotic mathematical models. These special solutions organize the general behavior of the other solutions. Thus, the investigation and the computation of these solutions are fundamental to understand and control the evolution of the dynamics. In this project of scientific initiation, we are interested in studying the invariant solutions of a 4D map aiming to learn tools for future applications in Astronautics. This will be achieved through the analysis of phase spaces, computation of Lyapunov exponent, implementation and application of Newton-Raphson method, in addition to the application of chaos control strategies.