scholarly journals New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time Integration

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
T. E. Simos
Keyword(s):  
Time Integration ◽  
Differential Method ◽  
Algebraic Order ◽  
Long Time ◽  
Long Time Integration ◽  
Differential Methods

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.

CLOSED NEWTON–COTES TRIGONOMETRICALLY-FITTED FORMULAE FOR LONG-TIME INTEGRATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1061-1074 ◽  
Author(s):  
T. E. SIMOS
Keyword(s):  
Symplectic Geometry ◽  
Equations Of Motion ◽  
Time Integration ◽  
Symplectic Integrators ◽  
Symplectic Methods ◽  
Long Time ◽  
One Step ◽  
Long Time Integration ◽  
Differential Methods ◽  
Symplectic Schemes

The connection between closed Newton–Cotes, trigonometrically-fitted differential methods and symplectic integrators is investigated in this paper. It is known from the literature that several one-step symplectic integrators have been obtained based on symplectic geometry. However, the investigation of multistep symplectic integrators is very poor. Zhu et al.2 presented the well known open Newton–Cotes differential methods as multilayer symplectic integrators. Chiou and Wu2 also investigated the construction of multistep symplectic integrators based on the open Newton–Cotes integration methods. In this paper we investigate the closed Newton–Cotes formulae and we write them as symplectic multilayer structures. After this we construct trigonometrically-fitted symplectic methods which are based on the closed Newton–Cotes formulae. We apply the symplectic schemes in order to solve Hamilton's equations of motion which are linear in position and momentum. We observe that the Hamiltonian energy of the system remains almost constant as integration procceeds.

scholarly journals Clutter Cancellation and Long Time Integration for GNSS-Based Passive Bistatic Radar

2021 ◽  
Vol 13 (4) ◽  
pp. 701 ◽  
Author(s):  
Binbin Wang ◽  
Hao Cha ◽  
Zibo Zhou ◽  
Bin Tian
Keyword(s):  
Fourier Transform ◽  
Target Detection ◽  
Time Integration ◽  
Detection Performance ◽  
Bistatic Radar ◽  
Detection Range ◽  
Robust Detection ◽  
Coherent Integration ◽  
Long Time ◽  
Long Time Integration

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.

Review on critical technology development of avian radar system

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Weishi Chen ◽  
Yifeng Huang ◽  
Xianfeng Lu ◽  
Jie Zhang
Keyword(s):  
Technology Development ◽  
Time Integration ◽  
Radar System ◽  
Content Type ◽  
Advantages And Disadvantages ◽  
Detection And Tracking ◽  
Critical Technology ◽  
Long Time ◽  
Long Time Integration ◽  
Target Characteristics

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.

scholarly journals Variational Integrators in Holonomic Mechanics

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1358
Author(s):  
Shumin Man ◽  
Qiang Gao ◽  
Wanxie Zhong
Keyword(s):  
Variational Principle ◽  
Dynamic Systems ◽  
Time Integration ◽  
Quadrature Rule ◽  
Quadrature Rules ◽  
Variational Integrators ◽  
Lagrange Polynomials ◽  
Holonomic Constraints ◽  
Long Time ◽  
Long Time Integration

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.

Nonlinear Dynamics of a Beam-Rigid Body Microgyroscope

2014 ◽  
Author(s):  
S. A. M. Lajimi ◽  
G. R. Heppler ◽  
E. Abdel-Rahman
Keyword(s):  
Nonlinear Dynamics ◽  
Rigid Body ◽  
Shooting Method ◽  
Electrostatic Force ◽  
Time Integration ◽  
Primary Resonance ◽  
Longitudinal Axis ◽  
Response Curves ◽  
Long Time ◽  
Long Time Integration

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.

scholarly journals Geometric Numerical Integration in Ecological Modelling

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 25 ◽  
Author(s):  
Fasma Diele ◽  
Carmela Marangi
Keyword(s):  
Numerical Integration ◽  
Time Integration ◽  
Continuous Model ◽  
Ecological Models ◽  
Ecological Modelling ◽  
Geometric Numerical Integration ◽  
Qualitative Properties ◽  
Long Time ◽  
Numerical Integrators ◽  
Long Time Integration

A major neglected weakness of many ecological models is the numerical method used to solve the governing systems of differential equations. Indeed, the discrete dynamics described by numerical integrators can provide spurious solution of the corresponding continuous model. The approach represented by the geometric numerical integration, by preserving qualitative properties of the solution, leads to improved numerical behaviour expecially in the long-time integration. Positivity of the phase space, Poisson structure of the flows, conservation of invariants that characterize the continuous ecological models are some of the qualitative characteristics well reproduced by geometric numerical integrators. In this paper we review the benefits induced by the use of geometric numerical integrators for some ecological differential models.

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