Long-time Integration of Non-Stiff and Oscillatory Hamiltonian Systems

Ernst Hairer ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
2021 ◽  
Vol 13 (4) ◽  
pp. 701 ◽  
Binbin Wang ◽  
Hao Cha ◽  
Zibo Zhou ◽  
Bin Tian

Clutter cancellation and long time integration are two vital steps for global navigation satellite system (GNSS)-based bistatic radar target detection. The former eliminates the influence of direct and multipath signals on the target detection performance, and the latter improves the radar detection range. In this paper, the extensive cancellation algorithm (ECA), which projects the surveillance channel signal in the subspace orthogonal to the clutter subspace, is first applied in GNSS-based bistatic radar. As a result, the clutter has been removed from the surveillance channel effectively. For long time integration, a modified version of the Fourier transform (FT), called long-time integration Fourier transform (LIFT), is proposed to obtain a high coherent processing gain. Relative acceleration (RA) is defined to describe the Doppler variation results from the motion of the target and long integration time. With the estimated RA, the Doppler frequency shift compensation is carried out in the LIFT. This method achieves a better and robust detection performance when comparing with the traditional coherent integration method. The simulation results demonstrate the effectiveness and advantages of the proposed processing method.

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
T. E. Simos

The closed Newton-Cotes differential methods of high algebraic order for small number of function evaluations are unstable. In this work, we propose a new closed Newton-Cotes trigonometrically fitted differential method of high algebraic order which gives much more efficient results than the well-know ones.

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Weishi Chen ◽  
Yifeng Huang ◽  
Xianfeng Lu ◽  
Jie Zhang

Purpose This paper aims to review the critical technology development of avian radar system at airports. Design/methodology/approach After the origin of avian radar technology is discussed, the target characteristics of flying birds are analyzed, including the target echo amplitude, flight speed, flight height, trajectory and micro-Doppler. Four typical airport avian radar systems of Merlin, Accipiter, Robin and CAST are introduced. The performance of different modules such as antenna, target detection and tracking, target recognition and classification, analysis of bird information together determines the detection ability of avian radar. The performances and key technologies of the ubiquitous avian radar are summarized and compared with other systems, and their applications, deployment modes, as well as their advantages and disadvantages are introduced and analyzed. Findings The ubiquitous avian radar achieves the long-time integration of target echoes, which greatly improves detection and classification ability of the targets of birds or drones, even under strong background clutter at airport. In addition, based on the big data of bird situation accumulated by avian radar, the rules of bird activity around the airport can be mined to guide the bird avoidance work. Originality/value This paper presented a novel avian radar system based on ubiquitous digital radar technology. The authors’ experience has confirmed that this system can be effective for airport bird strike prevention and management. In the future, the avian radar system will see continued improvement in both software and hardware, as the system is designed to be easily extensible.

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1358
Shumin Man ◽  
Qiang Gao ◽  
Wanxie Zhong

Variational integrators for dynamic systems with holonomic constraints are proposed based on Hamilton’s principle. The variational principle is discretized by approximating the generalized coordinates and Lagrange multipliers by Lagrange polynomials, by approximating the integrals by quadrature rules. Meanwhile, constraint points are defined in order to discrete the holonomic constraints. The functional of the variational principle is divided into two parts, i.e., the action of the unconstrained term and the constrained term and the actions of the unconstrained term and the constrained term are integrated separately using different numerical quadrature rules. The influence of interpolation points, quadrature rule and constraint points on the accuracy of the algorithms is analyzed exhaustively. Properties of the proposed algorithms are investigated using examples. Numerical results show that the proposed algorithms have arbitrary high order, satisfy the holonomic constraints with high precision and provide good performance for long-time integration.

S. A. M. Lajimi ◽  
G. R. Heppler ◽  
E. Abdel-Rahman

The nonlinear dynamics of a cantilever-beam-rigid-body MEMS gyroscope near primary resonance are studied by using a shooting method and long time integration. The microsensor includes a square beam carrying an eccentric end-rigid-body rotating about the longitudinal axis and under an electrostatic force. The mathematical model of the system is reduced by using the method of assumed modes. Using a shooting method and long time integration, the dynamic characteristics of the system are investigated and presented in terms of frequency-response plots and force-response curves. The bifurcation points are discussed and the regions of instability are characterized.

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