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 |
Divergent Instability, Handling, Steady Mode, Two-Link Road Train
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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
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
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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Download@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}
}
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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