Talk 4

Title: Electrogravitational Dynamics of an Charged Material Particle under the Action of Two Fixed Electric Charges on the Earth's Surface

Speaker:  Hugo Guimarães

Affiliation: Universidade Federal de Pernambuco (UFPE)

Abstract:  In this work, we study the dynamics, in real three-dimensional space, of a material particle with an electric charge under the action of its weight and the electrostatic forces induced by two fixed charges located on a vertical axis. We make strong use of the concept of stability in the sense of Lyapunov and, in this direction, we look at the eigenvalues of the Hessian matrix of the Hamiltonian system in question, as well as the concept of orbital stability.  We use symplectic transformations to obtain Hamiltonians in a rotating coordinate system and the reduction of the number of degrees of freedom of the Hamiltonian system in question to simplify the studied equation. This work is based on the latest developments by ProfessorHildeberto Cabral in the theory of Hamiltonian systems which are contained in his book with Professor Lúcia Brandão, "Normal Forms and Stability of Hamiltonian Systems", published by Springer in 2023.