Home / Journals / CMES / Vol.111, No.1, 2016
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  • Open Access

    ARTICLE

    Low Thrust Minimum Time Orbit Transfer Nonlinear Optimization Using Impulse Discretization via the Modified Picard–Chebyshev Method

    Darin Koblick1,2,3, Shujing Xu4, Joshua Fogel5, Praveen Shankar1
    CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.1, pp. 1-27, 2016, DOI:10.3970/cmes.2016.111.001
    Abstract The Modified Picard-Chebyshev Method (MPCM) is implemented as an orbit propagation solver for a numerical optimization method that determines minimum time orbit transfer trajectory of a satellite using a series of multiple impulses at intermediate waypoints. The waypoints correspond to instantaneous impulses that are determined using a nonlinear constrained optimization routine, SNOPT with numerical force models for both Two-Body and J2 perturbations. It is found that using the MPCM increases run-time performance of the discretized lowthrust optimization method when compared to other sequential numerical solvers, such as Adams-Bashforth-Moulton and Gauss-Jackson 8th order methods. More >

  • Open Access

    ARTICLE

    Enhancements to Modified Chebyshev-Picard Iteration Efficiency for Perturbed Orbit Propagation

    B. Macomber1, A. B. Probe1, R. Woollands1, J. Read1, J. L. Junkins1
    CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.1, pp. 29-64, 2016, DOI:10.3970/cmes.2016.111.029
    Abstract Modified Chebyshev Picard Iteration is an iterative numerical method for solving linear or non-linear ordinary differential equations. In a serial computational environment the method has been shown to compete with, or outperform, current state of practice numerical integrators. This paper presents several improvements to the basic method, designed to further increase the computational efficiency of solving the equations of perturbed orbit propagation. More >

  • Open Access

    ARTICLE

    Efficient Orbit Propagation of Orbital Elements Using Modified Chebyshev Picard Iteration Method

    J.L. Read1, A. Bani Younes2, J.L. Junkins3
    CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.1, pp. 65-81, 2016, DOI:10.3970/cmes.2016.111.065
    Abstract This paper focuses on propagating perturbed two-body motion using orbital elements combined with a novel integration technique. While previous studies show that Modified Chebyshev Picard Iteration (MCPI) is a powerful tool used to propagate position and velocity, the present results show that using orbital elements to propagate the state vector reduces the number of MCPI iterations and nodes required, which is especially useful for reducing the computation time when including computationally-intensive calculations such as Spherical Harmonic gravity, and it also converges for > 5.5x as many revolutions using a single segment when compared with cartesian propagation. Results for the Classical… More >

  • Open Access

    ARTICLE

    Multidirectional Gaussian Mixture Models for Nonlinear Uncertainty Propagation

    V. Vittaldev1, R. P. Russell2
    CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.1, pp. 83-117, 2016, DOI:10.3970/cmes.2016.111.083
    Abstract Monte Carlo simulations are an accurate but computationally expensive procedure for approximating the resultant non-Gaussian probability density function (PDF) after propagation of an initial Gaussian PDF through a nonlinear function. Univariate splitting libraries for Gaussian Mixture Models (GMMs) exist with up to five elements in the literature. The number of splits are extended in the present work by generating three homoscedastic univariate splitting libraries with up to 39 elements. Mulitvariate GMMs are typically handled with splits along a single direction. Instead, we generate a regular multidirectional grid over the initial multivariate Gaussian distribution by recursively applying the splitting library along… More >

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