A general computational method for the accurate calculation of rotationally and vibrationally excited states of tetraatomic molecules is developed. The resulting program is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. The program offers a choice of coordinate systems based on Radau, Jacobi, diatom–diatom and orthogonal satellite vectors. The method...

Over the last decade, pseudospectral (PS) computational methods for nonlinear constrained optimal control have been applied to many industrial-strength problems, notably the recent zero-propellant-maneuvering of the International Space Station performed by NASA. In this paper, we prove a theorem on the rate of convergence for the optimal cost computed using PS methods. It is a first proved conv...

In this paper a generalization of the indirect pseudo-spectral method, presented in [17], for numerical solution budget-constrained infinite horizon optimal control problems is presented. Consideration problem statement framework weighted functional spaces allows to arrive at good approximation initial value adjoint variable, which inevitable obtaining solutions. The method illustrated by apply...

Rapid and accurate rendezvous proximity operations for spacecraft are crucial to the success of most space missions. In this paper, a sequential convex programming method, combined with first-order second-order Birkhoff pseudospectral methods, is proposed autonomous spacecraft. The original nonlinear nonconvex close-range problem thrust constraints no-fly zone converted into its version by usin...

This paper is concerned with the approximation of matrix functionals defined by a large, sparse or structured, symmetric definite matrix. These functionals are Stieltjes integrals with a measure supported on a compact real interval. Rational Gauss quadrature rules that are designed to exactly integrate Laurent polynomials with a fixed pole in the vicinity of the support of the measure may yield...

We adopt a multidomain pseudospectral method to analyze lamellar gratings for general conical diffraction from TE and TM diffractions. The validity and usefulness of this approach are demonstrated through normal metallic lossy and highly conductive lossless gratings. The developed method provides excellent numerical stability and convergence over commonly used rigorous couple wave analysis (RCW...