scholarly journals Direct Trajectory Optimization by a Chebyshev Pseudospectral Method

2002 ◽  
Vol 25 (1) ◽  
pp. 160-166 ◽  
Author(s):  
Fariba Fahroo ◽  
I. Michael Ross
Keyword(s):  
Trajectory Optimization ◽  
Pseudospectral Method ◽  
Chebyshev Pseudospectral Method ◽  
Chebyshev Pseudospectral

scholarly journals Efficient Convex Optimization of Reentry Trajectory via the Chebyshev Pseudospectral Method

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Chun-Mei Yu ◽  
Dang-Jun Zhao ◽  
Ye Yang
Keyword(s):  
Trajectory Optimization ◽  
Normal Load ◽  
Dynamic Pressure ◽  
Pseudospectral Method ◽  
Convex Programming Problem ◽  
Convex Constraints ◽  
Chebyshev Pseudospectral Method ◽  
Reentry Trajectory ◽  
Reentry Trajectory Optimization ◽  
Chebyshev Pseudospectral

A novel sequential convex (SCvx) optimization scheme via the Chebyshev pseudospectral method is proposed for efficiently solving the hypersonic reentry trajectory optimization problem which is highly constrained by heat flux, dynamic pressure, normal load, and multiple no-fly zones. The Chebyshev-Gauss Legend (CGL) node points are used to transcribe the original dynamic constraint into algebraic equality constraint; therefore, a nonlinear programming (NLP) problem is concave and time-consuming to be solved. The iterative linearization and convexification techniques are proposed to convert the concave constraints into convex constraints; therefore, a sequential convex programming problem can be efficiently solved by convex algorithms. Numerical results and a comparison study reveal that the proposed method is efficient and effective to solve the problem of reentry trajectory optimization with multiple constraints.

scholarly journals Prediction of Dynamic Stability Using Mapped Chebyshev Pseudospectral Method

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Jae-Young Choi ◽  
Dong Kyun Im ◽  
Jangho Park ◽  
Seongim Choi
Keyword(s):  
Unsteady Flow ◽  
Three Dimensional ◽  
Pseudospectral Method ◽  
Accurate Method ◽  
Spectral Approach ◽  
Fourier Pseudospectral Method ◽  
Chebyshev Pseudospectral Method ◽  
Fourier Pseudospectral ◽  
Chebyshev Pseudospectral ◽  
Good Agreement

A mapped Chebyshev pseudospectral method is extended to solve three-dimensional unsteady flow problems. As the classical Chebyshev spectral approach can lead to numerical instabilities due to ill conditioning of the spectral matrix, the Chebyshev points are evenly redistributed over the domain by an inverse sine mapping function. The mapped Chebyshev pseudospectral method can be used as an alternative time-spectral approach that uses a Chebyshev collocation operator to approximate the time derivative terms in the unsteady flow governing equations, and the method can make general applications to both nonperiodic and periodic problems. In this study, the mapped Chebyshev pseudospectral method is employed to solve three-dimensional periodic problem to verify the spectral accuracy and computational efficiency with those of the Fourier pseudospectral method and the time-accurate method. The results show a good agreement with both of the Fourier pseudospectral method and the time-accurate method. The flow solutions also demonstrate a good agreement with the experimental data. Similar to the Fourier pseudospectral method, the mapped Chebyshev pseudospectral method approximates the unsteady flow solutions with a precise accuracy at a considerably effective computational cost compared to the conventional time-accurate method.

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