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Handling Analysis and Defining Conditions of Dangerous-Sfe Divergent Stability Loss of a Two-Link Road Train Nonlinear Model

Received: 20 March 2018     Accepted: 2 May 2018     Published: 24 May 2018
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Abstract

Road train steady motion mode divergent stability loss compiles with the critical according to A.M. Liapunov case of a single zero root. That said both safe and dangerous stability loss scenarios are possible according to N.N. Bautin. Dangerous stability loss is followed with a semi-trailer intensive drifting even in case of linear motion. Analyzing the reasons of such system behavior requires developing new effective analytical approaches towards defining safe-dangerous articulated vehicle divergent stability loss because direct methods for finding corresponding Liapunov indexes may appear ineffective in the analytical form being excessively cumbersome. The work presents a formalized approach to analyzing safe stability loss conditions the essence of which is in defining conditions when bifurcation set structure rearrangement occurs in linear motion critical speed small neighborhood. The kind of approach has been tested by the authors when analyzing single unit vehicle stability. Analytical relations are presented defining road train configuration following circular paths with constant Ackermann angle; consideration of analytical results accuracy evaluation is performed based on comparing to the results received with numerical analytic parameter continuation method; analytical relations are received corresponding to safe linear motion mode stability loss (in the sense of N.N. Bautin). The work develops methods of analyzing two-link vehicle non-linear model two-parameter steady modes manifold stability.

Published in Mathematical Modelling and Applications (Volume 3, Issue 2)
DOI 10.11648/j.mma.20180302.11
Page(s) 31-38
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Divergent Instability, Handling, Steady Mode, Two-Link Road Train

References
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[3] Vo-Duy Thanh, C Ta Minh. A universal dynamic and kinematic model of vehicles. In Vehicle Power and Propulsion Conference (VPPC), 2015 IEEE, pages 1–6.
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[5] Gillespie, Thomas D. Fundamentals of Vehicle Dynamics. Society of Automotive Engineers, Inc. 1992, p. 470.
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[10] Troger, H., Zeman, K. A nonlinear analysis of the generic types of loss of stability of the steady state motion of the tractor – semitrailer. Vehicle System Dynamics, 1984, vol. 13, № 4, pp. 161-172.
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[14] Bautin, N. N. Behaviour of Dynamical Systems near the Boundery of the Stability Domain. Moscow: Nauka, 1984.
[15] Verbitskii, V. G., Lobas, L. G. Effect of external mechanical loads on the steady motions of wheeled machines. Applied Mechanics, 1990, № 7, pp. 97-102.
[16] Verbitskii, V. G., Lobas, L. G. Bifurcation of steady states of an assemblage of absolutely rigid and rolling elastic bodies. Izv. ASUSSR, MTT, 1991, № 3, pp. 30-37.
[17] Verbitskii, V. G., Lobas, L. G. Bifurcations of steady states in systems with rolling under constant force perturbations. Applied Mathematics and Mechanics, 1994, № 5, pp. 165-170.
[18] Pauwelussen, J. P. Analysis and prevention of excessive lateral behaviour of articulated vehicles. XII International Heavy Truck Conference, 13-15 September 1995, Budapest, Hungary.
[19] Ellis, J. R. Vehicle Dynamics. Moscow: Mashinostroenie, 1975, pp. 216 (Russian translation).
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Cite This Article
  • APA Style

    Verbitskii Vladimir Grigorievich, Bezverhyi Anatoliy Igorevich, Tatievskyi Dmitry Nikolayevich. (2018). Handling Analysis and Defining Conditions of Dangerous-Sfe Divergent Stability Loss of a Two-Link Road Train Nonlinear Model. Mathematical Modelling and Applications, 3(2), 31-38. https://doi.org/10.11648/j.mma.20180302.11

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    ACS Style

    Verbitskii Vladimir Grigorievich; Bezverhyi Anatoliy Igorevich; Tatievskyi Dmitry Nikolayevich. Handling Analysis and Defining Conditions of Dangerous-Sfe Divergent Stability Loss of a Two-Link Road Train Nonlinear Model. Math. Model. Appl. 2018, 3(2), 31-38. doi: 10.11648/j.mma.20180302.11

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    AMA Style

    Verbitskii Vladimir Grigorievich, Bezverhyi Anatoliy Igorevich, Tatievskyi Dmitry Nikolayevich. Handling Analysis and Defining Conditions of Dangerous-Sfe Divergent Stability Loss of a Two-Link Road Train Nonlinear Model. Math Model Appl. 2018;3(2):31-38. doi: 10.11648/j.mma.20180302.11

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  • @article{10.11648/j.mma.20180302.11,
      author = {Verbitskii Vladimir Grigorievich and Bezverhyi Anatoliy Igorevich and Tatievskyi Dmitry Nikolayevich},
      title = {Handling Analysis and Defining Conditions of Dangerous-Sfe Divergent Stability Loss of a Two-Link Road Train Nonlinear Model},
      journal = {Mathematical Modelling and Applications},
      volume = {3},
      number = {2},
      pages = {31-38},
      doi = {10.11648/j.mma.20180302.11},
      url = {https://doi.org/10.11648/j.mma.20180302.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20180302.11},
      abstract = {Road train steady motion mode divergent stability loss compiles with the critical according to A.M. Liapunov case of a single zero root. That said both safe and dangerous stability loss scenarios are possible according to N.N. Bautin. Dangerous stability loss is followed with a semi-trailer intensive drifting even in case of linear motion. Analyzing the reasons of such system behavior requires developing new effective analytical approaches towards defining safe-dangerous articulated vehicle divergent stability loss because direct methods for finding corresponding Liapunov indexes may appear ineffective in the analytical form being excessively cumbersome. The work presents a formalized approach to analyzing safe stability loss conditions the essence of which is in defining conditions when bifurcation set structure rearrangement occurs in linear motion critical speed small neighborhood. The kind of approach has been tested by the authors when analyzing single unit vehicle stability. Analytical relations are presented defining road train configuration following circular paths with constant Ackermann angle; consideration of analytical results accuracy evaluation is performed based on comparing to the results received with numerical analytic parameter continuation method; analytical relations are received corresponding to safe linear motion mode stability loss (in the sense of N.N. Bautin). The work develops methods of analyzing two-link vehicle non-linear model two-parameter steady modes manifold stability.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Handling Analysis and Defining Conditions of Dangerous-Sfe Divergent Stability Loss of a Two-Link Road Train Nonlinear Model
    AU  - Verbitskii Vladimir Grigorievich
    AU  - Bezverhyi Anatoliy Igorevich
    AU  - Tatievskyi Dmitry Nikolayevich
    Y1  - 2018/05/24
    PY  - 2018
    N1  - https://doi.org/10.11648/j.mma.20180302.11
    DO  - 10.11648/j.mma.20180302.11
    T2  - Mathematical Modelling and Applications
    JF  - Mathematical Modelling and Applications
    JO  - Mathematical Modelling and Applications
    SP  - 31
    EP  - 38
    PB  - Science Publishing Group
    SN  - 2575-1794
    UR  - https://doi.org/10.11648/j.mma.20180302.11
    AB  - Road train steady motion mode divergent stability loss compiles with the critical according to A.M. Liapunov case of a single zero root. That said both safe and dangerous stability loss scenarios are possible according to N.N. Bautin. Dangerous stability loss is followed with a semi-trailer intensive drifting even in case of linear motion. Analyzing the reasons of such system behavior requires developing new effective analytical approaches towards defining safe-dangerous articulated vehicle divergent stability loss because direct methods for finding corresponding Liapunov indexes may appear ineffective in the analytical form being excessively cumbersome. The work presents a formalized approach to analyzing safe stability loss conditions the essence of which is in defining conditions when bifurcation set structure rearrangement occurs in linear motion critical speed small neighborhood. The kind of approach has been tested by the authors when analyzing single unit vehicle stability. Analytical relations are presented defining road train configuration following circular paths with constant Ackermann angle; consideration of analytical results accuracy evaluation is performed based on comparing to the results received with numerical analytic parameter continuation method; analytical relations are received corresponding to safe linear motion mode stability loss (in the sense of N.N. Bautin). The work develops methods of analyzing two-link vehicle non-linear model two-parameter steady modes manifold stability.
    VL  - 3
    IS  - 2
    ER  - 

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Author Information
  • Department of Computerized System Software, Faculty of Power Engineering, Electronics and Information Technologies, Zaporizhia State Engineering Academy, Zaporizhia, Ukraine

  • Department of Computerized System Software, Faculty of Power Engineering, Electronics and Information Technologies, Zaporizhia State Engineering Academy, Zaporizhia, Ukraine

  • Department of Computerized System Software, Faculty of Power Engineering, Electronics and Information Technologies, Zaporizhia State Engineering Academy, Zaporizhia, Ukraine

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