Engineering topics
Publications and source records attributed to Lefton, L..
A process for adjusting perturbation magnitude for accurate difference-quotient estimation of derivatives is described. The process is intended to be carried out sequentially, alternating with iterations of a parameter-optimization algorithm. A more complex and computationally-expensive scheme for occasional auxiliary use is also described.
Barrier surface construction in the joint space of the differential turning game for thrust-vectored vs. conventional aircraft is discussed. Differential-turn studies are based on modifications of existing computer programs including an energy-turn program, and one which generates hodograph data. Optimal turning flight in energy approximation is discussed for the conventional aircraft configurations. It is concluded that any advantages realized from thrust-vectoring are minor, unless hover is possible, where advantages would be major at low energies, and affect tactics at high energies as well.
An approach to one-on-one air-combat analysis is described which employs discrete gaming of a parameterized model featuring choice between several closed-loop control policies. A preference-ordering formulation due to Falco is applied to rational choice between outcomes: win, loss, mutual capture, purposeful disengagement, draw. Approximate optimization is provided by an active-cell scheme similar to Falco's obtained by a 'backing up' process similar to that of Kopp. The approach is designed primarily for short-duration duels between craft with large-envelope weaponry. Some illustrative computations are presented for an example modeled using constant-speed vehicles and very rough estimation of energy shifts.
Gradient projection is a powerful algorithm for minimization of a function subject to constraints. Constraint nonlinearities hamper projection computations. The constraints must then be restored before another projection cycle. The restoration steps taken in the process of following nonlinear constraint surfaces can be used as a guide to the construction of a curve which more nearly follows the constraints than does the straight line in the projected gradient direction. This scheme, termed 'curvilinear projection', was explored in earlier research. The study presently reported carries out some computational experiments using a related version of the technique. Some other details of projection computations which turn out to be practically important are taken up: rules for updating the variable metric in projection when early termination of the one-dimensional search on constraint violation occurs, and active-constraint logic for screening inequalities that makes use of the Kuhn-Tucker necessary conditions.
A chase in a horizontal plane between a pursuer with a large capture radius and a more maneuverable evading vehicle is examined with constant-speed vehicle models. An approximation to the 'sidestepping' maneuver of the Homicidal Chauffeur Game is modified to account for the effect of evader turning rate, and an estimate of capture radius required is so obtained which agrees remarkably well with Cockayne's point-capture result. The maneuver assumes central importance for barrier surfaces appearing in the Game of Two Cars. Results are given for required weapon capture-radius in terms of the maneuverability of the two vehicles. Some calculations of capture radius are presented.
The numerical analysis of composite differential-turn trajectory pairs was studied for 'fast-evader' and 'neutral-evader' attitude dynamics idealization for attack aircraft. Transversality and generalized corner conditions are examined and the joining of trajectory segments discussed. A criterion is given for the screening of 'tandem-motion' trajectory segments. Main focus is upon the computation of barrier surfaces. Fortunately, from a computational viewpoint, the trajectory pairs defining these surfaces need not be calculated completely, the final subarc of multiple-subarc pairs not being required. Some calculations for pairs of example aircraft are presented. A computer program used to perform the calculations is included.
The computation of composite differential-turn trajectory pairs is studied for 'fast-evader' and 'neutral-evader' idealizations introduced in earlier publications. Transversality and generalized corner conditions are examined and the joining of trajectory segments discussed. A criterion is given for the screening of 'tandem-motion' trajectory segments. Main focus is upon the computation of barrier surfaces. Fortunately, from a computational viewpoint, the trajectory pairs defining these surfaces need not be calculated completely, the final subarc of multiple-subarc pairs not being required. Some calculations for pairs of example aircraft are presented.
A variable-metric algorithm is described that uses both linear and quadratic penalty terms for handling nonlinear constraints. Quadratic penalty coefficients are adjusted in a process which maintains a positive-definite matrix of second partial derivatives of the function without generating the large positive eigenvalues which cause zigzagging and slow convergence. The schemes suggested use inferred second-order properties not only in terms of the variable metric of the Davidson-Fletcher-Powell algorithm (or its relatives) but by estimating of second directional derivatives by fitting cubics to various functions along search directions.
Modified program has been developed using improved variation of Encke method which avoids accumulation of round-off errors and avoids numerical ambiguities arising from near-circular orbits of low inclination. Variety of interplanetary trajectory problems can be computed with maximum accuracy and efficiency.
Modifications to interplanetary trajectory program for providing capability of generating optimum low-thrust trajectory in N-body field
Interplanetary trajectory Encke method FORTRAN program manual for IBM 360 computer
Interplanetary trajectories Encke method program manual
Orbit calculation using Encke perturbation method and Fortran IV programming