Reference : Universal functions in the study of the relative orbital dynamics
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Engineering, computing & technology : Aerospace & aeronautics engineering
Universal functions in the study of the relative orbital dynamics
Condurache, Daniel mailto [Department of Theoretical Mechanics, Technical University Gheorghe Asachi, 700050, Iasi, Romania]
Martinusi, Vladimir mailto [Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux >]
Advances in the Astronautical Sciences
1st International Academy of Astronautics Conference on Dynamics and Control of Space Systems, DyCoSS 2012
19 March 2012 through 21 March 2012
[en] Closed form solutions ; Gravitational fields ; Kepler equation ; Non-linear model ; Orbital dynamics ; Relative motion ; Relative orbit ; Universal functions ; Astronomy
[en] The closed-form solution to the problem of the relative motion in gravitational fields is expressed with the help of the universal functions. The full nonlinear model of the relative motion is considered, and no linearization or approximation assumptions are made. The results are free of singularities and they hold for any reference and targeted orbits, as well as for any time scale. A unified way to propagate the relative orbit with respect to time is introduced, by making use of the solution to a generalized Kepler equation.

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