Abstract
Variational method is applied to the state equations in order to derive the costate equations and their boundary conditions. Thereafter, the analyses of the eigenvalues of the state and costate equations are performed. It is shown that the eigenvalues of the Jacobean matrices of the state and the transposed Jacobean matrices of the costate equations are analytically and numerically the same. Based on the eigenvalue analysis, the costate equations with their boundary conditions are numerically integrated. Numerical results of the eigenvalues problems of the state and costate equations and of a maximization problem are finally presented.
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Acknowledgements
This work was supported through FAR Grant NAG-4-165 by the NASA Dryden Flight Research Center and through Cooperative Agreement NCC1–68 by the NASA Langley Research Center. Dr. K. K. Gupta was the technical monitor for the NASA Dryden NAG-4-165 grant.
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Ibrahim, A.H., Tiwari, S.N. A variational method in design optimization and sensitivity analysis for aerodynamic applications. Engineering with Computers 20, 88–95 (2004). https://doi.org/10.1007/s00366-004-0273-7
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DOI: https://doi.org/10.1007/s00366-004-0273-7