Stability solutions of a dumbbell-like system in an elliptical orbit

17th Brazilian Colloquium on Orbital Dynamics

Souza Dos Santos, Denilson Paulo^1,2 ; Da Rocha E Brito De Aguiã Morant, Simão António^1 ; Guerman, Anna D.^1 ; Burov, Alexander A.^3

Centre for Mechanical and Aerospace Science and Technologies (C-MAST), UBI, Portugal^1

Division of Space Mechanics and Control, INPE (National Institute for Space Research), São José dos Campos, SP, Brazil^2

Dorodnotsyn Computing Center, Russian Academy of Sciences, Russia^3

关键词: Chaotic properties;    Dynamic behaviors;    Elliptical orbits;    Gravitational fields;    Lagrangian formulations;    Length variations;    Numerical simulators;    Stability condition;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/641/1/012004/pdf
DOI  :  10.1088/1742-6596/641/1/012004

来源: IOP

【 摘 要 】

A dumbbell-like system is analyzed, considering two mass points connected with a massless and rigid tether with length variations, and the center of mass described by Keplerian orbits. This kind of system, in a certain type of configuration, is a simple conceptualization of the space elevator. The system motion is obtained with the Lagrangian Formulation in a Central Gravitational Field, and the perturbations of motion are neglected. Laws of control are considered for the angle of systems rotation around the center of mass. Those include uniform rotations or no rotation at all. Stability conditions were obtained for the first case, analyzing its neighborhood and using Floquet Theory. The results shown there are regions of eccentricities were stability is found. Lastly, a dynamic numerical simulator was created, where the implementation of the results could be tested. The dynamic behavior of the system showed regular and chaotic properties.