This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System’s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transfor...

Article history: Received 10 December 2012 Received in revised form 26 July 2013 Accepted 30 July 2013 Available online 17 August 2013

An initial value problem with piecewise constant coefficients is considered. The accuracies for both finite difference methods and the pseudospectral method are analyzed, and a modification of the initial value problem is suggested. The modified problem is shown to have the same temporal period as the original problem does, and a second order accuracy is obtained for the pseudospectral method a...

presents a modiied Chebyshev pseudospec-tral method, involving mapping of the Chebyshev points, for solving rst-order hyperbolic initial boundary value problems. It is conjectured that the time step restriction for the modiied method is O(N ?1) compared to O(N ?2) for the standard Chebyshev pseudospectral method, where N is the number of discretization points in space. In the present paper we s...

Of the many direct numerical methods, the pseudospectral method serves as an effective tool to solve the reentry trajectory optimization for hypersonic vehicles. However, the traditional pseudospectral method is time-consuming due to large number of discretization points. For the purpose of autonomous and adaptive reentry guidance, the research herein presents a multistage trajectory control st...

Multivariate global polynomial approximations – such as polynomial chaos or stochastic collocation methods – are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses a numerical integration rule to approximate the Fourier-type coefficients of a truncated expansion in orthogonal polynomials. For problems in more than two ...

A short discussion of optimal control methods is presented including indirect, direct shooting, and direct transcription methods. Next the basics of multiple-interval pseudospectral methods are given independent of the numerical scheme to highlight the fundamentals. The two numerical schemes discussed are the Legendre pseudospectral method with LGL nodes and the Chebyshev pseudospectral method ...

The post-optimality analysis of a tetrahedral formation flying optimal control problem is considered. In particular, this four-spacecraft orbit insertion problem is transcribed to a nonlinear programming problem (NLP) using a direct method called the Gauss pseudospectral method. The Karush-Kuhn-Tucker (KKT) conditions for this NLP are then derived and are compared to the conditions obtained via...

A Fourier pseudospectral time-domain method is applied to wave propagation problems pertinent to computational aeroacoustics. The original algorithm of the Fourier pseudospectral timedomain method works for periodical problems without the interaction with physical boundaries. In this paper we develop a slip wall boundary condition, combined with buffer zone technique to solve some non-periodica...