Efficient algorithm for nonlinear trajectory optimization of spacecraft using generating functions

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Using a recently developed technique based on Hamilton-Jacobi theory, we develop a method to approximate the solution of the Hamilton-Jacobi equation which can solve nonlinear trajectory optimization of spacecraft. The proposed method is based on the successive approximation and Galerkin spectral method with Chebyshev polynomials. This approach is expected to derive the analytical solution of the optimal control problem in the large domain.