A Study on the Stability of a Ballistic System Under Random Excitation

2016 ◽  
Vol 15 (04) ◽  
pp. 1650026 ◽  
Author(s):  
Chunyan Yang ◽  
Lina Xu ◽  
Yong Huang
Keyword(s):  
Bifurcation Diagram ◽  
Pitch Angle ◽  
Linear Part ◽  
Random Excitation ◽  
Dynamical Theory ◽  
Deterministic System ◽  
Random Disturbance ◽  
Eigenvalue Method ◽  
And Performance ◽  
The Stability

The stability analysis of a ballistic system is important for its design and performance. The eigenvalue method is presented to get the stability of the linear part of the ballistic system. Combining the eigenvalue method and stochastic dynamical theory, we can get the bifurcation diagram of the pitch angle for the deterministic system and the bifurcation diagram for the system with random disturbance. By comparing the two situations, the dynamic behavior at the feature point was analyzed.

scholarly journals On the classification of homoclinic attractors of three-dimensional flows

2019 ◽  
Vol 21 (4) ◽  
pp. 443-459
Author(s):  
Alexey O. Kazakov ◽  
Efrosiniia Y. Karatetskaia ◽  
Alexander D. Kozlov ◽  
Klim A. Safonov
Keyword(s):  
Dynamical Systems ◽  
Equilibrium State ◽  
Bifurcation Diagram ◽  
Continuous Time ◽  
Linear Part ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Structure And Properties ◽  
The Stability

For three-dimensional dynamical systems with continuous time (flows), a classification of strange homoclinic attractors containing an unique saddle equilibrium state is constructed. The structure and properties of such attractors are determined by the triple of eigenvalues of the equilibrium state. The method of a saddle charts is used for the classification of homoclinic attractors. The essence of this method is in the construction of an extended bifurcation diagram for a wide class of three-dimensional flows (whose linearization matrix is written in the Frobenius form). Regions corresponding to different configurations of eigenvalues are marked in this extended bifurcation diagram. In the space of parameters defining the linear part of the considered class of three-dimensional flows bifurcation surfaces bounding 7 regions are constructed. One region corresponds to the stability of the equilibrium states while other 6 regions correspond to various homoclinic attractors of the following types: Shilnikov attractor, 2 types of spiral figure-eight attractors, Lorenz- like attractor, saddle Shilnikov attractor and attractor of Lyubimov-Zaks-Rovella. The paper also discusses questions related to the pseudohyperbolicity of homoclinic attractors of three-dimensional flows. It is proved that only homoclinic attractors of two types can be pseudohyperbolic: Lorenz-like attractors containing a saddle equilibrium with a two-dimensional stable manifold whose saddle value is positive and saddle Shilnikov attractors containing a saddle equilibrium state with a two-dimensional unstable manifold.

scholarly journals Analytical Modeling and Design of Novel Conical Halbach Permanent Magnet Couplings for Underwater Propulsion

2021 ◽  
Vol 9 (3) ◽  
pp. 290
Author(s):  
Yukai Li ◽  
Yuli Hu ◽  
Youguang Guo ◽  
Baowei Song ◽  
Zhaoyong Mao
Keyword(s):  
Permanent Magnet ◽  
Analytical Calculation ◽  
Underwater Propulsion ◽  
Conical Structure ◽  
Torque Analysis ◽  
Dynamic Seal ◽  
And Performance ◽  
The Stability ◽  
Propulsion Unit ◽  
Force Calculation

Permanent magnet couplings can convert a dynamic seal into a static seal, thereby greatly improving the stability of the underwater propulsion unit. In order to make full use of the tail space and improve the transmitted torque capability, a conical Halbach permanent magnet coupling (C-HPMC) is proposed in this paper. The C-HPMC combines multiple cylindrical HPMCs with different sizes into an approximately conical structure. Compared with the conical permanent magnet couplings in our previous work, the novel C-HPMC has better torque performance and is easy to process. The analytical calculation method of transmitted torque of C-HPMC is proposed on the basis of torque calculation of the three common types of HPMCs. The accuracy of the torque calculation of the three HPMCs is verified, and the torque performance of the three HPMCSs of different sizes is compared and discussed. The “optimal type selection” method is proposed and applied in the design of C-HPMC. Finally, on the basis of torque analysis calculation and axial force calculation, a complete flowchart of the design and performance analysis of C-HPMC is described.

scholarly journals Modelling and Stability Analysis of Articulated Vehicles

2021 ◽  
Vol 11 (8) ◽  
pp. 3663
Author(s):  
Tianlong Lei ◽  
Jixin Wang ◽  
Zongwei Yao
Keyword(s):  
Stability Analysis ◽  
Critical Velocity ◽  
Equations Of State ◽  
Steering System ◽  
Analysis Model ◽  
Nonlinear Dynamic Model ◽  
Equilibrium Equations ◽  
Eigenvalue Method ◽  
Articulated Vehicles ◽  
The Stability

This study constructs a nonlinear dynamic model of articulated vehicles and a model of hydraulic steering system. The equations of state required for nonlinear vehicle dynamics models, stability analysis models, and corresponding eigenvalue analysis are obtained by constructing Newtonian mechanical equilibrium equations. The objective and subjective causes of the snake oscillation and relevant indicators for evaluating snake instability are analysed using several vehicle state parameters. The influencing factors of vehicle stability and specific action mechanism of the corresponding factors are analysed by combining the eigenvalue method with multiple vehicle state parameters. The centre of mass position and hydraulic system have a more substantial influence on the stability of vehicles than the other parameters. Vehicles can be in a complex state of snaking and deviating. Different eigenvalues have varying effects on different forms of instability. The critical velocity of the linear stability analysis model obtained through the eigenvalue method is relatively lower than the critical velocity of the nonlinear model.

Adaptive attitude-tracking control of spacecraft considering on-orbit refuelling

2020 ◽  
pp. 014233122097313
Author(s):  
Yiqi Xu
Keyword(s):  
Tracking Control ◽  
Closed Loop ◽  
Closed Loop System ◽  
Tracking Errors ◽  
Attitude Tracking ◽  
Control Scheme ◽  
Inertia Model ◽  
And Performance ◽  
Attitude Tracking Control ◽  
The Stability

This paper studies the attitude-tracking control problem of spacecraft considering on-orbit refuelling. A time-varying inertia model is developed for spacecraft on-orbit refuelling, which actually includes two processes: fuel in the transfer pipe and fuel in the tank. Based upon the inertia model, an adaptive attitude-tracking controller is derived to guarantee the stability of the resulted closed-loop system, as well as asymptotic convergence of the attitude-tracking errors, despite performing refuelling operations. Finally, numerical simulations illustrate the effectiveness and performance of the proposed control scheme.

scholarly journals Characterization of Cocycle Attractors for Nonautonomous Reaction–Diffusion Equations

2016 ◽  
Vol 26 (08) ◽  
pp. 1650135 ◽  
Author(s):  
C. A. Cardoso ◽  
J. A. Langa ◽  
R. Obaya
Keyword(s):  
Chaotic Dynamics ◽  
Linear Part ◽  
Reaction Diffusion ◽  
Positive Cone ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Minimal Set ◽  
Full Characterization ◽  
The Stability

In this paper, we describe in detail the global and cocycle attractors related to nonautonomous scalar differential equations with diffusion. In particular, we investigate reaction–diffusion equations with almost-periodic coefficients. The associated semiflows are strongly monotone which allow us to give a full characterization of the cocycle attractor. We prove that, when the upper Lyapunov exponent associated to the linear part of the equations is positive, the flow is persistent in the positive cone, and we study the stability and the set of continuity points of the section of each minimal set in the global attractor for the skew product semiflow. We illustrate our result with some nontrivial examples showing the richness of the dynamics on this attractor, which in some situations shows internal chaotic dynamics in the Li–Yorke sense. We also include the sublinear and concave cases in order to go further in the characterization of the attractors, including, for instance, a nonautonomous version of the Chafee–Infante equation. In this last case we can show exponentially forward attraction to the cocycle (pullback) attractors in the positive cone of solutions.

Nondestructive Test on Typical Roadway Supports of a Mine via Drilling Core and Ground Penetrating Radar

2011 ◽  
Vol 368-373 ◽  
pp. 2411-2416
Author(s):  
Jian Ping Han ◽  
Hai Peng Liu
Keyword(s):  
Ground Penetrating Radar ◽  
Geological Structure ◽  
Surrounding Rock ◽  
Potential Threat ◽  
Real Performance ◽  
Design Requirements ◽  
And Performance ◽  
The Stability ◽  
Ground Penetrating ◽  
Drilling Core

Temporary or permanent supports are necessary in underground construction for maintaining the stability and limiting the damage of surrounding rock. Due to the uncertainty of geological structure, the specificity of the underground environment as well as other factors, the quality and performance of supporting structure are often difficult to satisfy the design requirements, which not only seriously affects the normal construction and operation of mines but also has the potential threat to the safety of underground production. In order to investigate the influence of the unfavorable geologic environment on supporting concrete and evaluate the real performance of roadway supports of a mine, 17 typical projects were chosen and the strength of supporting concrete was detected by nondestructive drilling core method. The result shows that the strength is widely less than the design value. Furthermore, 4 projects of them were investigated by the ground penetrating radar (GPR) in order to evaluate the feasibility of GPR in the performance investigation of the roadway supports of a mine. The results indicate that ground penetrating radar is capable of measuring the thickness of the support, the distribution of rebars and the defects of the surrounding rock.

Map Width Enhancement Technique for a Turbocharger Compressor

2013 ◽  
Vol 136 (6) ◽  
Author(s):  
Subenuka Sivagnanasundaram ◽  
Stephen Spence ◽  
Juliana Early
Keyword(s):  
Performance Improvement ◽  
Peak Pressure ◽  
Pressure Ratio ◽  
Comparison Study ◽  
Heavy Duty ◽  
Recirculating Flow ◽  
Heavy Duty Diesel ◽  
And Performance ◽  
The Stability ◽  
The Impact

This paper presents an investigation of map width enhancement and the performance improvement of a turbocharger compressor using a series of static vanes in the annular cavity of a classical bleed slot system. The investigation has been carried out using both experimental and numerical analysis. The compressor stage used for this study is from a turbocharger unit used in heavy duty diesel engines of approximately 300 kW. Two types of vanes were designed and added to the annular cavity of the baseline classical bleed slot system. The purpose of the annular cavity vane technique is to remove some of the swirl that can be carried through the bleed slot system, which would influence the pressure ratio. In addition to this, the series of cavity vanes provides a better guidance to the slot recirculating flow before it mixes with the impeller main inlet flow. Better guidance of the flow improves the mixing at the inducer inlet in the circumferential direction. As a consequence, the stability of the compressor is improved at lower flow rates and a wider map can be achieved. The impact of two cavity vane designs on the map width and performance of the compressor was highlighted through a detailed analysis of the impeller flow field. The numerical and experimental study revealed that an effective vane design can improve the map width and pressure ratio characteristic without an efficiency penalty compared to the classical bleed slot system without vanes. The comparison study between the cavity vane and noncavity vane configurations presented in this paper showed that the map width was improved by 14.3% due to a significant reduction in surge flow and the peak pressure ratio was improved by 2.25% with the addition of a series of cavity vanes in the annular cavity of the bleed slot system.

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