Yang Cheng, Bin Jia, Ming Xin

The International Conference on Computational & Experimental Engineering and Sciences, Vol.16, No.2, pp. 33-34, 2011, DOI:10.3970/icces.2011.016.033

Abstract A sparse grid approach to orbit uncertainty propagation is presented. Efficient and accurate uncertainty propagation methods for nonlinear dynamic systems have been of enormous interest to space object tracking. Recent methods include those based on the time evolution of the probability density function, the statistical moments, the random samples, or a sum of Gaussian components. The idea of the sparse grid method for orbit uncertainty propagation is to represent the initial uncertainty by a sparse grid, propagate the sparse grid points individually through the nonlinear orbit dynamics, and compute the statistical moments from the propagated sparse grid points. The Smolyak… More >

Shigenori Tanaka¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.13, No.3, pp. 61-62, 2009, DOI:10.3970/icces.2009.013.061

Abstract Recent developments in ab initio calculations for biomolecular systems such as proteins and nucleic acids are illustrated on the basis of the fragment molecular orbital (FMO) method. Examples of the calculated systems include nuclear receptors with small ligands, cAMP receptor protein complexed with DNA, influenza virus hemagglutinin complexes, and bioluminescent oxyluciferin-luciferase complex. Quantitative calculations with the inclusion of relevant electron correlation effects have well reproduced those experimental results concerning the binding affinity, the mutation effects, the emission spectra, and so on. Feasibility of massively parallel computations with the FMO method is also discussed. More >

Renyong Zhang

The International Conference on Computational & Experimental Engineering and Sciences, Vol.21, No.2, pp. 22-24, 2019, DOI:10.32604/icces.2019.04656

Abstract This article aims to give a method for the fast numerical computation and continuation of families of periodic orbits in the strong nonlinear circular restricted three-body problem, and we focus our attention on those in the Earth-moon system. This work is primarily motivated by a series of missions and plans that take advantages of the three-body periodic orbits associated with the collinear equilibrium points, L1, L2 and L3 or two gravitational celestial bodies. We describe the method used that allows to follow individual families of periodic orbits by numerical continuation, which based on Jacobi energy surface, of strong nonlinear equations.… More >

Qianxin Wang^1,2,3, Chao Hu^1,2,*, Ya Mao^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.117, No.3, pp. 509-525, 2018, DOI:10.31614/cmes.2018.04098

Abstract Designing the optimal distribution of Global Navigation Satellite System (GNSS) ground stations is crucial for determining the satellite orbit, satellite clock and Earth Rotation Parameters (ERP) at a desired precision using a limited number of stations. In this work, a new criterion for the optimal GNSS station distribution for orbit and ERP determination is proposed, named the minimum Orbit and ERP Dilution of Precision Factor (OEDOP) criterion. To quickly identify the specific station locations for the optimal station distribution on a map, a method for the rapid determination of the selected station locations is developed, which is based on the… More >

Xiaoli Bai¹, John L. Junkins²

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.2, pp. 129-146, 2016, DOI:10.3970/cmes.2016.111.129

Abstract This paper presents Modified Chebyshev-Picard Iteration (MCPI) methods for long-term integration of the coupled orbit and attitude dynamics. Although most orbit predictions for operational satellites have assumed that the attitude dynamics is decoupled from the orbit dynamics, the fully coupled dynamics is required for the solutions of uncontrolled space debris and space objects with high area-to-mass ratio, for which cross sectional area is constantly changing leading to significant change on the solar radiation pressure and atmospheric drag. MCPI is a set of methods for solution of initial value problems and boundary value problems. The methods refine an orthogonal function approximation… More >

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 >

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 >

Darin Koblick^1,2,3, 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 >

Chein-Shan Liu ^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.2, pp. 73-94, 2007, DOI:10.3970/cmes.2007.017.073

Abstract The primary objectives of the present exposition focus on five different types of representations of the plastic equations obtained from an elastic-perfectly plastic model by employing different corotational stress rates. They are (a) an affine nonlinear system with a finite-dimensional Lie algebra, (b) a canonical linear system in the Minkowski space, (c) a non-canonical linear system in the Minkowski space, (d) the Lie-Poisson bracket formulation, and (e) a two-generator and two-bracket formulation. For the affine nonlinear system we prove that the Lie algebra of the vector fields is so(5,1), which has dimensions fifteen, and by the Lie theory the superposition… More >

R. Savino¹, V. Carandente¹

FDMP-Fluid Dynamics & Materials Processing, Vol.8, No.4, pp. 453-476, 2012, DOI:10.3970/fdmp.2012.008.453

Abstract A new small recoverable re-entry capsule with deployable heat shield is analyzed. The possible utilization of the capsule is for safe Earth return of science payloads or data from low Earth orbit at an inexpensive cost, taking advantage of its deployable structure to perform an aerobraking re-entry mission, with relatively low heat and mechanical loads. The system concept for the heat shield is based on umbrella-like frameworks and existing ceramic fabrics. An aerothermodynamic analysis is developed to show that the peak heat flux, for a capsule with a ballistic coefficient lower than 10 kg/m², is in the range 250-350 kW/m²… More >