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By Jean-Pierre Marec
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Extra resources for Optimal Space Trajectories
2 Optimization of low-thrust (LT) systems The mass breakdown of an electric propulsion system (Fig. 4) can be roughly written as follows : F= qW -m=q W P=LqW 2 2 Fig. 4 Eleotvio propulsion system. o initial m = m f final + "P + = propellant m useful G + m power S »T structure + + V tank propellant (payload) generator with the approximate relations : = k m , T p cS ~ »ο m = α = (α/η) Ρ G Gmax max where α is the mass per unit power of the generator (a - 3 to 30 kg/kW for a m = s m 16 nuclear-electric system according to the value of P ç m a x ) anc ^ n is ejector t n e efficiency.
Cy considered as the characteristic velocity necessary for the given mission : Cy - h (W, τ) Cj/V - fe (W V), T s REFERENCES 1. L. CROCCO, Space Flight, Princeton Lectures (unpublished), 1963. 2. L. GRODZOVSKII, Variational problems in space flight mechanics, J0TA 3 4 (1969) 44. 3. L. N. KIFORENKO, Weight limitation influence on opti mum motion parameters of a body of variable mass, in Lectures Notes in Astronautics No, 112 Λ 4. Springer - Verlag, 1970. P. CONTENSOU, Etude théorique des trajectoires optimales dans un champ de gravitation - Application au cas d'un centre d'attraction unique, Astronaut.
We can also say that, at time t, the proba bilities of using point Mi and M2 are respectively l-λ and λ. From the kine matic point of view, this process is equivalent to using, during the interval τ, the imaginary operating point M, being the barycenter of Mi and M2 at which we place the masses l-λ and λ respectively. Fig. 8 Natural rectilinear part. 0 *2 Fig. 9 Artificial rectilinear part. M 45 This assumption of "relaxation" of the control makes it possible for us to deal with an artificial rectilinear part (Fig.