Spacecraft formation flying dynamics and control using the geomagnetic lorentz force

Shu Tsujii, Mai Bando, Hiroshi Yamakawa

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


The motion of a charged satellite subjected to the Earth's magnetic field is considered. The Lorentz force, which acts on a charged particle when it is moving through a magnetic field, provides a new concept of propellantless electromagnetic propulsion. A dynamic model of a charged satellite, including the effect of the Lorentz force in the vicinity of a circular or an elliptic orbit, is derived and its application to formation flying is considered. Based on Hill-Clohessy-Wiltshire equations and Tschauner-Hempel equations, analytical approximations for the relative motion in Earth orbit are obtained. The analysis based on the linearized equations shows the controllability of the system by stepwise charge control. The sequential quadratic programming method is applied to solve the orbital transfer problem of the original nonlinear equations in which the analytical solutions cannot be obtained.Astrategy to reduce the charge amount using sequential quadratic programming is also developed.

Original languageEnglish
Pages (from-to)136-148
Number of pages13
JournalJournal of Guidance, Control, and Dynamics
Issue number1
Publication statusPublished - 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Aerospace Engineering
  • Space and Planetary Science
  • Electrical and Electronic Engineering
  • Applied Mathematics


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