Talk 7

Title: Laura-Andoyer equations for central configurations

Speaker:  Thiago Dias

Affiliation: Professor,  Universidade Federal Rural de Pernambuco de Pernambuco

Abstract: In this talk we study the equivalence between Laura-Andoyer equations and the central configuration equations. G. Meyer derives Laura-Andoyer equations in the planar and spatial cases. Hagihara proves the equivalence between Laura-Andoyer equations and central configuration equations in the planar in the case when the center of mass is at the origin. Hamptom and Santropete derive a generalization of the Laura-Andoyer equations for central configurations of all dimensions. We derive generalized Laura-Andoyer equations very similar to the ones obtained by Hampton and Santropete. Our contribution is to prove that the generalized Laura-Andoyer equations are equivalent to the central configuration equations for each choice of the number of bodies and the dimension. lastly, we discuss applications of Laura-Andoyer equations for non-Dziobek central configurations.