Nonlinear dynamic of objects in space excited by the gravity potential

Author(s)

Maira Rosine Bolla

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Mecânica
• Defense date: 2005-07-28

Examining board members

Jose Manoel Balthazar; Eder Lima de Albuquerque

• Advisor: Jose Manoel Balthazar; Helder Anibal Hermini

Abstract

This work concerns of two parts, in the first we will make the study of the dynamics of dual-spin-spacecraft modeled by a simple mechanical system consisting of an unbalanced rotor attached to an elastic support and driven by non-ideal source. In the second part we will formulate the complete nonlinear differential equations governing the nonlinear motions of a beam able to undergo bending and pitching in space. The formulation is based on a variational principle and accounts for all the nonlinearities due to deformation and gravity gradient effects. The nonlinearities due to deformation arise due to geometric effects, which consist of nonlinear curvature and nonlinear inertia terms. Expanded equations governing the nonlinear perturbed motions about an equilibrium are also developed for the case when the beam is in circular orbit. Such equations are suited for a perturbation analysis of the motion, and nonlinearities up to cubic order in a bookkeeping parameter are retained in them. The coupled nonlinear pitch-bending response of a free-free beam in a circular orbit, when the beam is subjected to a periodic external excitation, is analysed too. The nonlinearities present in the differential equations of motion are due to deformations of the beam (i. e. curvature and inertia nonlinearities) and to the gravity-gradient moments. Perturbation methods are used to analyse the motion. Several resonant motions exhibited by the system are analysed in detail, namely, harmonic resonances when the frequency of the external excitations, O, is either near the natural frequency of the flexural or of the pitch motion, and a superharmonic resonance when O is near one half of the natural frequency for the pitch motion. The latter two resonances are associated with very low excitation frequencies (AU)