6533b835fe1ef96bd129eb6d
RESEARCH PRODUCT
Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
Jean-baptiste CaillauBernard Bonnardsubject
[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyIntegrable system02 engineering and technologyEnergy minimization01 natural sciencesHamiltonian systemsymbols.namesake020901 industrial engineering & automationBellman equationCircular orbit0101 mathematicsMathematical PhysicsComputingMilieux_MISCELLANEOUSMathematicsApplied Mathematics010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]symbolsSPHERESAstrophysics::Earth and Planetary Astrophysics[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Orbital maneuverHamiltonian (quantum mechanics)Analysisdescription
Abstract This article deals with the optimal transfer of a satellite between Keplerian orbits using low propulsion and is based on preliminary results of Epenoy et al. (1997) where the optimal trajectories of the energy minimization problem are approximated using averaging techniques. The averaged Hamiltonian system is explicitly computed. It is related to a Riemannian problem whose distance is an approximation of the value function. The extremal curves are analyzed, proving that the system remains integrable in the coplanar case. It is also checked that the metric associated with coplanar transfers towards a circular orbit is flat. Smoothness of small Riemannian spheres ensures global optimality of the computed extremals.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-01-01 |