Three-impulse transfer from lunar orbits.
Three-impulse orbital transfer from lunar orbits and earth reentry trajectory applications
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Three-impulse orbital transfer from lunar orbits and earth reentry trajectory applications
Three-impulse orbital transfer from lunar orbits and earth reentry trajectory applications
Impulse functions associated with two-impulse transfer between nearly tangent noncoapsidal coplanar elliptical orbits
Impulse orbital transfer for nearly tangent coplanar elliptical orbits
Two-impulse orbital transfer problem for elliptical orbits, describing techniques for finding optimum transfers and optimum rendezvous trajectories
Probability distribution errors effect in linear and planar impulse orbital transfers, considering angular orientation and impulsive velocity
A method has previously been developed to satisfy terminal rendezvous and intermediate timing constraints for planetary missions involving orbital operations. The method uses impulse factoring in which a two-impulse transfer is divided into three or four impulses which add one or two intermediate orbits. The periods of the intermediate orbits and the number of revolutions in each orbit are varied to satisfy timing constraints. Techniques are developed to retarget the orbital transfer in the presence of orbit-determination and maneuver-execution errors. Sample results indicate that the nominal transfer can be retargeted with little change in either the magnitude (Delta V) or location of the individual impulses. Additonally, the total Delta V required for the retargeted transfer is little different from that required for the nominal transfer. A digital computer program developed to implement the techniques is described.
Computational method for two impulse orbital transfer and rendezvous between two elliptical orbits
Quasi-linearization determination of optimum finite thrust and impulsive orbital transfers
Numerical and analytical results on optimum one impulse transfer between coplanar elliptical orbits
A method is presented for factoring a two-impulse orbital transfer into a three- or four-impulse transfer which solves the rendezvous problem and satisfies an intermediate timing constraint. Both the time of rendezvous and the intermediate time of a alinement are formulated as any element of a finite sequence of times. These times are integer multiples of a constant plus an additive constant. The rendezvous condition is an equality constraint, whereas the intermediate alinement is an inequality constraint. The two timing constraints are satisfied by factoring the impulses into collinear parts that vectorially sum to the original impulse and by varying the resultant period differences and the number of revolutions in each orbit. Five different types of solutions arise by considering factoring either or both of the two impulses into two or three parts with a limit for four total impulses. The impulse-factoring technique may be applied to any two-impulse transfer which has distinct orbital periods.
Optimal one- and two-impulse orbital transfer maneuvers, considering shallowly intersecting coplanar orbits
Analytic solution for minumum impulse transfer between two neighboring low eccentricity orbits
A multiple-impulse function is represented as a sequence of single-impulse functions. The single-impulse transfer which yields the velocity change required to transfer from a specified initial orbit to a partially specified final orbit is developed. Analytic derivatives of the function are obtained for use in optimization techniques. A four-impulse transfer is outlined. The analytic derivatives may allow more efficient optimization than numerical derivatives do.
Approximate analytical solution for minimum impulse transfer between circular orbit and given hyperbolic velocity vector at infinity
Analytic solution obtained for minimum impulse transfer between two neighboring low eccentricity orbits
Solutions are obtained for the two-impulse transfer of a vehicle between arbitrary inclined orbits in an inverse-square force field with the restriction that the magnitude of each of the two impulses has a fixed preassigned value. The two magnitudes need not be equal. The equations for the conservation of angular momentum and energy are augmented by the Laplace integral; these equations establish linear relationships between several of the variables. This set of linear equations and one of two quadratic equations constitute the analytically tractable part of the solution. The remaining part, consisting of finding the zeros (if they exist) of a single trigonometric function of one variable, is solved using numerical methods. Explicit lower bounds on each of the magnitudes of the two impulses are obtained by requiring the solution be real. Graphical results are presented to illustrate the solution.
First-order perturbation solution to problem of minimum-fuel orbit transfer in form of equal slope guidance constraint