Global trajectory targeting via computer graphics

A technique is described in which the two-point boundary value problem (TPBVP) may be solved with the aid of interactive computer graphics. The particular TPBVP considered is the optimal electric propulsion space trajectory problem. An appropriate two-dimensional projection of the TPBVP mapping, or trajectory, is displayed on the computer's television screen, and a man-in-the-loop varies selected trajectory starting conditions in the fashion of a nonlinear walk until the viewed trajectory endpoint lies near a displayed target. Once global targeting is accomplished in this manner, program internal logic can easily handle local targeting to strongly solve the TPBVP

Quasilocal energy and naked black holes

We extend the Brown and York notion of quasilocal energy to include coupled electromagnetic and dilaton fields and also allow for spatial boundaries that are not orthogonal to the foliation of the spacetime. We investigate how the quasilocal quantities measured by sets of observers transform with respect to boosts. As a natural application of this work we investigate the naked black holes of Horowitz and Ross calculating the quasilocal energies measured by static versus infalling observers.Comment: 5 pages, 1 figure; submitted to the 8th Canadian Conference on General Relativity and Relativistic Astrophysics. This paper is a condensed version of gr-qc/990707

Extension of the tridiagonal reduction (FEER) method for complex eigenvalue problems in NASTRAN

As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum were extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order was much lower than that of the full size problem. The reduction process was effected automatically, and thus avoided the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admitted mass, damping, and stiffness matrices which were unrestricted in character, i.e., they might be real, symmetric or nonsymmetric, singular or nonsingular

HILTOP supplement: Heliocentric interplanetary low thrust trajectory optimization program, supplement 1

Modifications and improvements are described that were made to the HILTOP electric propulsion trajectory optimization computer program during calendar years 1973 and 1974. New program features include the simulation of power degradation, housekeeping power, launch asymptote declination optimization, and powered and unpowered ballistic multiple swingby missions with an optional deep space burn

Heliocentric interplanetary low thrust trajectory optimization program, supplement 1, part 2

The improvements made to the HILTOP electric propulsion trajectory computer program are described. A more realistic propulsion system model was implemented in which various thrust subsystem efficiencies and specific impulse are modeled as variable functions of power available to the propulsion system. The number of operating thrusters are staged, and the beam voltage is selected from a set of five (or less) constant voltages, based upon the application of variational calculus. The constant beam voltages may be optimized individually or collectively. The propulsion system logic is activated by a single program input key in such a manner as to preserve the HILTOP logic. An analysis describing these features, a complete description of program input quantities, and sample cases of computer output illustrating the program capabilities are presented

Selected solar electric propulsion and ballistic missions studies

Selected missions using solar electric propulsion and conventional propulsion systems were studied. The accomplishment of the tasks required extensive modification of the trajectory optimization computer program HILTOP. In addition to adding new program features, HILTOP was completely restructured to reduce execution time. The specific mission studies reported on are the direct and Venus swingby missions to the comet Encke and solar electric propulsion missions to Encke and to a distance of 0.25 AU from the sun

Heliocentric interplanetary low thrust trajectory optimization program, supplement 1

The modifications and improvements made to the HILTOP electric propulsion trajectory optimization computer program up through the end of 1974 is described. New program features include the simulation of power degradation, housekeeping power, launch asymptote declination optimization, and powered and unpowered ballistic multiple swingby missions with an optional deep space burn. The report contains the new analysis describing these features, a complete description of program input quantities, and sample cases of computer output illustrating the new program capabilities