A modular, ion propelled, orbit transfer vehicle

A Low-Cost Launch Assistance System for Orbital Launch Vehicles

“…Among these, most researched was the interorbital tugs design. Cryogenic orbital storage [80,81], transfer [82], operation model [83][84][85], and interorbital tugs designs [86][87][88] were elaborated. But [89,90] was skeptical on feasibility of interorbital tugs.…”

Minimum-fuel lunar transfers with engine switching and transients

“…The MINLP method has a general problem statement of: min f{x,y) (2.4) x,y subject to: h{x,y) =0 (2.5) gix.y) >0 (2.6) yeY (2.7) where x, h, and g have the same dimension as the NLP problem and where y is a pvector within Y which is a set of integer variables. It's important to note that when finite bounds exist on the integer variables y, yL<y<yu (2.8) the integer variables can be expressed as binary, i.e., 0-1 variables, denoted by 2,-, by the following formula: y = J/L + + 2^2 + 4^3 + ... + 2'^^ (2)(3)(4)(5)(6)(7)(8)(9) where N is the minimum number of binary variables needed, and is given by N = l + INT log(yu -yt) log 2 (2.10) where INT indicates the integer tnmcation of the term in the brackets. This expression correspondence may not be practical for very large boimds, but the binary form of the integer variables is particxilarly applicable to this work which is described in Chapter 4.…”

“…An efficient method of finding this point is to search along a direction, </, whose norm is a minimum. This search direction can be determined by solving a least distance problem of the type: nun ^(Fd (2.1-3) subject to: Vhd + h =0 (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) Vgd + g >0 (2.15) Since this is a linear approximation model of the nonlinear constraints, it is prob able that the step>-size along this search direction will have to be varied to insure a decrease in the constraint error. A typical merit function to determine a step-size is to choose a step which reduces the constraint norm of the form, m, kl = |/i| + 5Imax(^.-,0) (2.16) t=i ([15], [16])…”

“…where ^ is the gravitational parameter for the attracting body, i.e., the Earth or Moon, a is the thrust acceleration defined by The Hamiltonian [28] is defined as H = L + X^f = \^f (3.11) where L = 0 since no integral term is in the performance index and / represents the dynamics of the system under consideration. The costate vector is given by A = [ Ar, Xg, Avp, Avfl (3.12) so the Hamiltoniaji becomes H = \,r + Xe6 + \vX + (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) Applying the stationcirity condition yields = 0 (/u)^ A = 0 a (Avr cos u -Avg sinu) = 0 (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) Canceling out and rearranging gives the classic "tangent steering law":…”