Computational and Applied Mathematics

, Volume 34, Issue 2, pp 521–534 | Cite as

Processing optimized for symmetry in the problem of evasive maneuvers

  • Antônio Delson C. de Jesus
  • Rafael Ribeiro de Sousa
Article

Abstract

The increasing number of space debris in operating regions around the earth constitutes a real threat to space missions. The goal of the research is to establish appropriate scientific-technological conditions to prevent the destruction and/or impracticability of spacecraft in imminent collision in these regions. A definitive solution to this problem has not yet been reached with the degree of precision that the dynamics of spatial objects (vehicle and debris) requires mainly due to the fact that collisions occur in chains and fragmentation of these objects in the space environment. This fact threatens the space missions on time and with no prospects for a solution in the near future. We present an optimization process in finding the initial conditions (CIC) to collisions, considering the symmetry of the distributions of maximum relative positions between spatial objects with respect to the spherical angles. For this, we used the equations of the dynamics on the Clohessy–Witshire, representing a limit of validation that is highly computationally costly. We simulate different maximum relative positions values of the corresponding initial conditions given in terms of spherical angles. Our results showed that there are symmetries that significantly reduce operating costs, such that the search of the CIC is advantageously carried out up to 4 times the initial processing routine. Knowledge of CIC allows the propulsion system operating vehicle implement evasive maneuvers before impending collisions with space debris.

Keywords

Symmetry Collision Maneuver evasive Space debris 

Mathematics Subject Classification

68Q17 

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2014

Authors and Affiliations

  • Antônio Delson C. de Jesus
    • 1
  • Rafael Ribeiro de Sousa
    • 2
  1. 1.Departamento de FísicaUniversidade Estadual de Feira de SantanaFeira de SantanaBrazil
  2. 2.Departamento de Matemática, Faculdade de Engenharia de GuaratinguetáUniversidade Estadual PaulistaGuaratinguetáBrazil

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