Nonlinear Dynamics

, 58:405 | Cite as

Nonlinear analysis of a simple model of temperature evolution in a satellite

  • José Gaite
  • Angel Sanz-Andrés
  • Isabel Pérez-Grande
Original Paper


We analyze a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential equation for the satellite’s temperature is analyzed by qualitative, perturbation and numerical methods, which prove that the temperature approaches a periodic pattern (attracting limit cycle). This approach can occur in two ways, according to the values of the parameters: (i) a slow decay towards the limit cycle over a time longer than the period, or (ii) a fast decay towards the limit cycle over a time shorter than the period. In the first case, an exactly soluble average equation is valid. We discuss the consequences of our model for the thermal stability of satellites.


Spacecraft thermal control Nonlinear oscillations Perturbation methods 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • José Gaite
    • 1
  • Angel Sanz-Andrés
    • 1
  • Isabel Pérez-Grande
    • 1
  1. 1.IDR/UPM, ETSI AeronáuticosUniversidad Politécnica de MadridMadridSpain

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