ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Research progress on nonlinear dynamic stability of aircraft landing system
Received date: 2024-09-18
Revised date: 2024-10-28
Accepted date: 2024-12-25
Online published: 2025-01-16
Supported by
National Natural Science Foundation of China(52172368);Natural Science Foundation of Jiangsu Province(BK20220135);Research Fund of State Key Laboratory of Mechanics and Control for Aerospace Structures （Nanjing University of Aeronautics and astronautics）(MCAS-I-0224G03);Spring Sunshine Program initiated by the Ministry of Education of China(HZKY20220126)
The issue of nonlinear dynamic stability in aircraft landing system has consistently posed a significant challenge in the design of both aircraft and landing gear systems， involving complex geometric nonlinearity， physical nonlinearity， and their interactions. Although the traditional time domain analysis method can effectively determine the stability， it exhibits limitation of high computational load in analyzing parameter influences and in achieving rapid and accurate parametric design. In recent years， the numerical continuation method has been widely applied in the field of nonlinear dynamic stability analysis of the landing system. This method enables rapid and precise analysis of the stability variation of the dynamic model with parameters， thereby significantly enhancing the design efficiency of aircraft and landing gear. Firstly， this paper describes the methods of dynamic stability， bifurcation analysis， and continuation calculation. Then， according to the functional classification of the landing system， the research status of the shimmy stability， taxiing direction stability， and retraction mechanism stability of the landing gear are summarized. The application research of bifurcation analysis methods and nonlinear dynamic stability based on the numerical continuation method in landing gear systems is mainly discussed. Finally， the research on the shimmy stability， taxiing direction stability， and retraction mechanism stability of aircraft landing gear is summarized and prospected.
Hong NIE , Xiaohui WEI , Ming ZHANG , Yin YIN , Qiaozhi YIN , Yong WANG . Research progress on nonlinear dynamic stability of aircraft landing system[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2025 , 46(5) : 531229 -531229 . DOI: 10.7527/S1000-6893.2024.31229
| 1 | European Union Aviation Safety Agency. Annual safety review 2024［M］. Cologne：European Union Aviation Safety Agency， 2024： 31-40. |
| 2 | SHARMA S， COETZEE E B， LOWENBERG M H， et al. Numerical continuation and bifurcation analysis in aircraft design： An industrial perspective［J］. Philosophical Transactions Series A， Mathematical， Physical， and Engineering Sciences， 2015， 373（2051）： 20140406. |
| 3 | FENG G， JIANG B Y， JIANG Y Y. Effect of multi-joint clearance coupling on shimmy of nose landing gear［J］. Aerospace， 2023， 10（11）： 911. |
| 4 | 印寅. 起落架收放动力学及可靠性研究［D］. 南京： 南京航空航天大学， 2017. |
| YIN Y. Study on dynamics and reliability of landing gear retraction［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2017 （in Chinese）. | |
| 5 | 刘晓媛. 新舟60飞机事故及不安全事件分析［C］∥航空安全与装备维修技术——航空安全与装备维修技术学术研讨会论文集， 2014： 424-429. |
| LIU X Y. Analysis of MA60 aircraft accidents and un-safe incidents ［C］∥Aviation Safety and Equipment Maintenance Technology Symposium， 2014：424-429 （in Chinese）. | |
| 6 | DOEDEL E J. AUTO： A program for the automatic bifurcation analysis of autonomous systems［J］. Congressus Numerantium， 1981， 30（265-284）：25-93. |
| 7 | COETZEE E， KRAUSKOPF B， LOWENBERG M. The dynamical systems toolbox： Integrating AUTO into MATLAB［C］∥16th US National Congress on Theoretical and Applied Mechanics， 2010. |
| 8 | COETZEE E. Modelling and nonlinear analysis of aircraft ground manoeuvres［D］. Bristol： University of Bristol， 2011. |
| 9 | GOVAERTS W， KUZNETSOV Y A， DHOOGEA. Numerical continuation of bifurcations of limit cycles in MATLAB［J］. SIAM Journal on Scientific Computing， 2005， 27（1）： 231-252. |
| 10 | DANKOWICZ H， SCHILDER F. An extended continuation problem for bifurcation analysis in the presence of constraints［C］?∥ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.New York：ASME， 2010： 311-321. |
| 11 | AHSAN Z， DANKOWICZ H， LI M W， et al. Methods of continuation and their implementation in the COCO software platform with application to delay differential equations［J］. Nonlinear Dynamics， 2022， 107（4）： 3181-3243. |
| 12 | SCHILDER F， BUREAU E， SANTOS I F， et al. Experimental bifurcation analysis： Continuation for noise-contaminated zero problems［J］. Journal of Sound and Vibration， 2015， 358： 251-266. |
| 13 | FORMICA G， ARENA A， LACARBONARA W， et al. Coupling FEM with parameter continuation for analysis of bifurcations of periodic responses in nonlinear structures［J］. Journal of Computational and Nonlinear Dynamics， 2013， 8（2）： 021013. |
| 14 | SIEBER J， KRAUSKOPF B. Control-based continuation of periodic orbits with a time-delayed difference scheme?［J］. International Journal of Bifurcation and Chaos， 2007， 17（8）： 2579-2593. |
| 15 | SIEBER J， KRAUSKOPF B. Control based bifurcation analysis for experiments［J］. Nonlinear Dynamics， 2008， 51（3）： 365-377. |
| 16 | BARTON D A W. Control-based continuation of a hybrid numerical/physical substructured system?［C］?∥Nonlinear Dynamics， Volume 1. Cham： Springer International Publishing， 2016： 203-207. |
| 17 | BARTON D A W， SIEBER J. Systematic experimental exploration of bifurcations with noninvasive control［J］. Physical Review E， 2013， 87（5）： 052916. |
| 18 | SIEBER J， KRAUSKOPF B， WAGG D， et al. Control-based continuation of unstable periodic orbits?［C］?∥ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. New York： ASME， 2010： 331-340. |
| 19 | RENSON L， SIEBER J， BARTON D A W， et al. Numerical continuation in nonlinear experiments using local Gaussian process regression［J］. Nonlinear Dynamics， 2019， 98（4）： 2811-2826. |
| 20 | LEE K H， BARTON D A W， RENSON L. Reduced-order modelling of flutter oscillations using normal forms and scientific machine learning［C］?∥Advances in Nonlinear Dynamics. Cham： Springer International Publishing， 2022： 49-63. |
| 21 | 苏二龙， 罗建军. 高超声速飞行器横侧向失稳非线性分岔分析［J］. 力学学报， 2016， 48（5）： 1192-1201. |
| SU E L， LUO J J. Nonlinear bifurcation analysis of lateral loss of stability for hypersonic vehicle［J］. Chinese Journal of Theoretical and Applied Mechanics， 2016， 48（5）： 1192-1201 （in Chinese）. | |
| 22 | 苏二龙， 罗建军， 闵昌万. 高超声速飞行器纵向大攻角非线性失稳分析与控制［J］. 航空学报， 2016， 37（）： 80-90. |
| SU E L， LUO J J， MIN C W. Analysis and control of nonlinear loss of stability for longitudinal flight dynamics of hypersonic vehicle with high angle of attack［J］. Acta Aeronautica et Astronautica Sinica， 2016， 37（Sup 1）： 80-90 （in Chinese）. | |
| 23 | 付军泉， 史志伟， 耿玺， 等. 基于试验分岔分析的翼身融合飞行器纵向稳定性［J］. 航空学报， 2022， 43（1）： 124931. |
| FU J Q， SHI Z W， GENG X， et al. Longitudinal stability of blended-wing-body aircraft based on experimental bifurcation analysis［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（1）： 124931 （in Chinese）. | |
| 24 | 卢京明. 某型飞机的前轮摆振分析与计算［J］. 飞机工程， 2001（3）： 14-20. |
| LU J M. Analysis and calculation of front wheel shimmy of an aircraft［J］. Aircraft Engineering， 2001（3）： 14-20 （in Chinese）. | |
| 25 | SURA N K， SURYANARAYAN S. Lateral stability of aircraft nose-wheel landing gear with closed-loop shimmy damper［J］. Journal of Aircraft， 2009， 46（2）： 505-509. |
| 26 | 刘胜利， 刘小川， 崔荣耀， 等. 机体连接处局部刚度对轻型飞机起落架摆振稳定性的影响研究［J］. 振动工程学报， 2017， 30（2）： 249-254. |
| LIU S L， LIU X C， CUI R Y， et al. The influence of the fuselage joint local stiffness on landing gear shimmy stabilization of the light aircraft［J］. Journal of Vibration Engineering， 2017， 30（2）： 249-254 （in Chinese）. | |
| 27 | ERET P， KENNEDY J， BENNETT G J. Effect of noise reducing components on nose landing gear stability for a mid-size aircraft coupled with vortex shedding and freeplay［J］. Journal of Sound and Vibration， 2015， 354： 91-103. |
| 28 | PADMANABHAN M A， DOWELL E H. Landing gear design/maintenance analysis for nonlinear shimmy［J］. Journal of Aircraft， 2015， 52（5）： 1707-1710. |
| 29 | 冯飞， 常正， 聂宏， 等. 飞机柔性对前起落架摆振的影响分析［J］. 航空学报， 2011， 32（12）： 2227-2235. |
| FENG F， CHANG Z， NIE H， et al. Analysis of influence of aircraft flexibility on nose landing gear shimmy［J］. Acta Aeronautica et Astronautica Sinica， 2011， 32（12）： 2227-2235 （in Chinese）. | |
| 30 | RAHMANI M， BEHDINAN K. Investigation on the effect of coulomb friction on nose landing gear shimmy［J］. Journal of Vibration and Control， 2019， 25（2）： 255-272. |
| 31 | RUAN S， ZHANG M， HONG Y， et al. Influence of clearance and structural coupling parameters on shimmy stability of landing gear［J］. The Aeronautical Journal， 2023， 127（1315）： 1591-1622. |
| 32 | THOTA P， KRAUSKOPF B， LOWENBERG M. Interaction of torsion and lateral bending in aircraft nose landing gear shimmy［J］. Nonlinear Dynamics， 2009， 57（3）： 455-467. |
| 33 | THOTA P， KRAUSKOPF B， LOWENBERG M H. Bifurcation analysis of aircraft nose landing gear shimmy with a dual-wheel configuration［C］?∥7th EUROMECH Solid Mechanics Conference. 2009. |
| 34 | HOWCROFT C， LOWENBERG M， NEILD S， et al. Effects of freeplay on dynamic stability of an aircraft main landing gear［J］. Journal of Aircraft， 2013， 50（6）： 1908-1922. |
| 35 | THOTA P， KRAUSKOPF B， LOWENBERG M. Multi-parameter bifurcation study of shimmy oscillations in a dual-wheel aircraft nose landing gear［J］. Nonlinear Dynamics， 2012， 70（2）： 1675-1688. |
| 36 | 冯广， 丁建宾， 姜义尧， 等. 轮胎刚度特性对大型民机前起落架摆振影响研究［J］. 航空工程进展， 2023， 14（2）： 55-64. |
| FENG G， DING J B， JIANG Y Y， et al. Research on influence of tire stiffness characteristics on shimmy of large civil aircraft nose landing gear［J］. Advances in Aeronautical Science and Engineering， 2023， 14（2）： 55-64 （in Chinese）. | |
| 37 | FENG F， NIE H， ZHANG M， et al. Effect of torsional damping on aircraft nose landing-gear shimmy［J］. Journal of Aircraft， 2015， 52（2）： 561-568. |
| 38 | RAHMANI M， BEHDINAN K. Parametric study of a novel nose landing gear shimmy damper concept［J］. Journal of Sound and Vibration， 2019， 457： 299-313. |
| 39 | WANG Y， JIN X Y， YIN Y. Using nonlinear feedback control to improve aircraft nose landing gear shimmy performance［J］. Meccanica， 2022， 57（9）： 2395-2411. |
| 40 | RUAN S， ZHANG M， YANG S F， et al. Research on the stability and bifurcation characteristics of a landing gear shimming dynamics system［J］. Aerospace， 2024， 11（2）： 104. |
| 41 | RAHMANI M， BEHDINAN K. Studying the effect of freeplay on nose landing gear shimmy using a fully nonlinear model［C］?∥ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.New York：ASME， 2018. |
| 42 | HOWCROFT C， LOWENBERG M， NEILD S， et al. Shimmy of an aircraft main landing gear with geometric coupling and mechanical freeplay［J］. Journal of Computational and Nonlinear Dynamics， 2015， 10（5）： 051011. |
| 43 | 张严. 考虑结构因素的起落架摆振稳定性分析［D］. 南京： 南京航空航天大学， 2018. |
| ZHANG Y. Stability analysis of landing gear shimmy considering structural factors［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2018 （in Chinese）. | |
| 44 | 阮爽， 张明， 聂宏. 结构间隙对起落架地面滑跑摆振特性影响分析［J］. 振动与冲击， 2024， 43（2）： 234-243. |
| RUAN S， ZHANG M， NIE H. Influence of the structural clearance on the shimmy characteristics of the landing gear during ground taxiing［J］. Journal of Vibration and Shock， 2024， 43（2）： 234-243 （in Chinese）. | |
| 45 | GAO X G， ZHENG Y C， DU X L， et al. Effect of clearance position of torque link structure on nose landing gear shimmy［J］. International Journal of Non-Linear Mechanics， 2024， 159： 104616. |
| 46 | RAHMANI M， BEHDINAN K. Interaction of torque link freeplay and Coulomb friction nonlinearities in nose landing gear shimmy scenarios?［J］. International Journal of Non-Linear Mechanics， 2020， 119： 103338. |
| 47 | RUAN S， ZHANG M， NIE H. Research and analysis of coulomb friction in landing gear shimmy?［J］. Journal of Aircraft， 2024， 61（4）： 1143-1154. |
| 48 | DU X L， XU Y， LIU Q， et al. Shimmy dynamics in a dual-wheel nose landing gear with freeplay under stochastic wind disturbances［J］. Nonlinear Dynamics， 2024， 112（4）： 2477-2499. |
| 49 | 冯飞. 起落架的摆振分支分析［D］. 南京： 南京航空航天大学， 2014. |
| FENG F. Bifurcation analysis of landing gear shimmy［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2014 （in Chinese）. | |
| 50 | 蔡佳圻. 飞机起落架摆振动力学分析及其非线性问题研究［D］. 南京： 南京航空航天大学， 2016. |
| CAI J Y. Mechanical analysis of aircraft landing gear pendulum vibration and its nonlinear problem research［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2016 （in Chinese）. | |
| 51 | CHENG L F， CAO H J， ZHANG L T. Two-parameter bifurcation analysis of an aircraft nose landing gear model［J］. Nonlinear Dynamics， 2021， 103（1）： 367-381. |
| 52 | 高相国， 卢翔， 单泽众. 考虑支柱轴向位移和纵向弯曲的双轮前起落架摆振特性分析［J/OL］. 振动工程学报， 2023： 1-12. （2023-11-16）. ， |
| LU X， SHAN Z Z. Analysis of shimmy characteristics of two-wheeled nose landing gear considering axial displacement and longitudinal bending of strut［J/OL］. China Industrial Economics， 2023： 1-12. （2023-11-16）. （in Chinese）. | |
| 53 | 冯飞， 罗波， 张策， 等. 轮间距与双轮共转对飞机起落架摆振的影响分析［J］. 振动与冲击， 2019， 38（6）： 212-217. |
| FENG F， LUO B， ZHANG C， et al. Effect of wheel-distance and corotating wheels on aircraft shimmy?［J］. Journal of Vibration and Shock， 2019， 38（6）： 212-217 （in Chinese）. | |
| 54 | 陈大伟. 起落架摆振的非线性分析及控制［D］. 南京： 南京航空航天大学， 2012. |
| CHEN D W. Nonlinear analysis and control of landing gear shimmy［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2012 （in Chinese）. | |
| 55 | JIANG Y Y， FENG G， TANG H H， et al. Effect of Coulomb friction on shimmy of nose landing gear under time-varying load?［J］. Tribology International， 2023， 188： 108828. |
| 56 | WANG Y， ZHANG T， YIN Y， et al. Reducing shimmy oscillation of a dual-wheel nose landing gear based on torsional nonlinear energy sink?［J］. Nonlinear Dynamics， 2024， 112（6）： 4027-4062. |
| 57 | 周家才， 赵艳影， 肖相志， 等. 非线性能量汇提高前起落架摆振的稳定性和抑制效果［J］. 固体力学学报， 2024， 45（6）： 759-775. |
| ZHOU J C， ZHAO Y Y， XIAO X Z， et al. Nose landing gear stability enhancement and shimmy suppression with a nonlinear energy sink［J］. Chinese Journal of Solid Mechanics， 2024， 45（6）： 759-775 （in Chinese）. | |
| 58 | 高泽迥， 林宏，赵世春，等.飞机地面载荷若干问题的探讨［J］.航空学报，1994， 15（1）：8-16. |
| GAO Z J. LIN H， ZHAO S C，et al. The development and discussion of some questions of aircraft ground loads［J］. Acta Aeronautica et Astronautica Sinica， 1994， 15（1）：8-16 （in Chinese）. | |
| 59 | SONG L， YANG H， YAN X F， et al. A study of instability in a miniature flying-wing aircraft in high-speed taxi［J］. Chinese Journal of Aeronautics， 2015， 28（3）： 749-756. |
| 60 | PLAKHTIENKO N P， SHIFRIN B M. Mechanical phenomena in ground run of an aircraft with near-critical slip angles?［J］. International Applied Mechanics， 2006， 42（6）： 714-720. |
| 61 | ABE M. A theoretical analysis on vehicle cornering behaviors in acceleration and in braking［J］. Vehicle System Dynamics， 2007， 15（sup1）： 1-14. |
| 62 | BARNES A， YAGER T. Simulation of aircraft behaviour on and close to the ground［R］. Washington，D.C.：AGARD， 1985. |
| 63 | ABZUG M J. Directional stability and control during landing rollout?［J］. Journal of Aircraft， 1999， 36（3）： 584-590. |
| 64 | 顾宏斌. 飞机地面运行的动力学模型［J］. 航空学报， 2001， 22（2）： 163-167. |
| GU H B. Dynamic model of aircraft ground handling［J］. Acta Aeronautica et Astronautica Sinica， 2001， 22（2）： 163-167 （in Chinese）. | |
| 65 | 朱丹丹， 贾玉红. 飞机过度/不足转向地面转弯操纵特性分析［J］. 北京航空航天大学学报， 2011， 37（12）： 1594-1598. |
| ZHU D D， JIA Y H. Analysis of oversteer/understeer characteristics of aircraft ground steering［J］. Journal of Beijing University of Aeronautics and Astronautics， 2011， 37（12）： 1594-1598 （in Chinese）. | |
| 66 | HOU Y X， GUAN Y L， JIA H G. Research on motion characteristics for UAV ground maneuvers?［C］?∥2015 IEEE International Conference on Mechatronics and Automation （ICMA）. Piscataway： IEEE Press， 2015： 22-26. |
| 67 | GU H B， GAO Z J. Landing gear shimmy and directional stability of aircraft undergoing non-straight taxiing［J］. Chinese Journal of Aeronautics 2001，14（2）：73-77. |
| 68 | LIANG T T， YIN Q Z， WEI X H. Effects of landing gear layout on the safe rollout envelope of equipped-skid aircraft［J］. Aerospace Science and Technology， 2022， 122： 107434. |
| 69 | 邱东海， 马伍元， 段镇， 等. 无人机地面操纵转弯特性分析与计算研究［J］. 飞行力学， 2015， 33（4）： 310-314. |
| QIU D H， MA W Y， DUAN Z， et al. Research on UAV ground handled steering characteristics analysis and calculation methods［J］. Flight Dynamics， 2015， 33（4）： 310-314 （in Chinese）. | |
| 70 | HE X F， AI J L. Taxiing stability verification and airworthiness certification for amphibious aircraft［J］. Science China Information Sciences， 2018， 62（1）： 10207. |
| 71 | 徐梓尧， 王琪. 含单边非完整约束飞机滑跑的建模与仿真方法［J］. 北京航空航天大学学报， 2015， 41（5）： 835-840. |
| XU Z Y， WANG Q. Method for modeling and simulation of aircraft taxiing with unilateral and non-holonomic constraints［J］. Journal of Beijing University of Aeronautics and Astronautics， 2015， 41（5）： 835-840 （in Chinese）. | |
| 72 | KHAPANE P D. Simulation of asymmetric landing and typical ground maneuvers for large transport aircraft［J］. Aerospace Science and Technology， 2003， 7（8）： 611-619. |
| 73 | 张震， 贾玉红. 无人机地面滑跑方向稳定性模糊控制研究［J］. 飞机设计， 2016， 36（2）： 18-21. |
| ZHANG Z， JIA Y H. Application of fuzzy control in UAV on-ground directional control system［J］. Aircraft Design， 2016， 36（2）： 18-21 （in Chinese）. | |
| 74 | ZHANG M， NIE H， WEI X H， et al. Modeling and simulation of aircraft anti-skid braking and steering using co-simulation method?［J］. COMPEL-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering， 2009， 28（6）： 1471-1488. |
| 75 | GAMEZ A， AL-QADI I L. Turning maneuver effect on near-surface airfield pavement responses［J］. Transportation Research Record： Journal of the Transportation Research Board， 2019， 2673（8）： 275-283. |
| 76 | COETZEE E， KRAUSKOPF B， LOWENBERG M. Nonlinear aircraft ground dynamics?［C］?∥International Conference on Nonlinear Problems in Aviation and Aerospace， 2006：1-8. |
| 77 | HORIUCHI S， OKADA K， NOHTOMI S. Analysis of accelerating and braking stability using constrained bifurcation and continuation methods［J］. Vehicle System Dynamics， 2008， 46（sup1）： 585-597. |
| 78 | RANKIN J， COETZEE E， KRAUSKOPF B， et al. Bifurcation and stability analysis of aircraft turning on the ground［J］. Journal of Guidance， Control， and Dynamics， 2009， 32（2）： 500-511. |
| 79 | RANKIN J， KRAUSKOPF B， LOWENBERG M， et al. Operational parameter study of aircraft dynamics on the ground［J］. Journal of Computational and Nonlinear Dynamics， 2010， 5（2）： 021007. |
| 80 | COETZEE E， KRAUSKOPF B， LOWENBERG M. Continuation analysis of aircraft ground loads during high-speed turns?［J］. Journal of Aircraft， 2012， 50（1）： 217-231. |
| 81 | COETZEE E， KRAUSKOPF B， LOWENBERG M. Application of bifurcation methods to the prediction of low-speed aircraft ground performance［J］. Journal of Aircraft， 2010， 47（4）： 1248-1255. |
| 82 | YIN Q Z， WEI X H， NIE H， et al. Parameter effects on high-speed UAV ground directional stability using bifurcation analysis?［J］. Chinese Journal of Aeronautics， 2021， 34（11）： 1-14. |
| 83 | MA Z Y， ZHU X P， ZHOU Z. Taxiing characteristic analysis and control for full-wing solar-powered unmanned aerial vehicle［J］. Journal of Northwestern Polytechnical University， 2019， 37（1）： 7-12. |
| 84 | KRAWCZYK M， ZAJDEL A. Automatic taxi directional control system for general aviation aircraft［J］. Journal of KONES. 2018； 25（3）： 299-306. |
| 85 | 贾伟， 孙哲芃， 吴玉生， 等. 基于L1方法的某型无人机滑跑纠偏控制［J］. 弹箭与制导学报， 2021， 41（1）： 48-52. |
| JIA W， SUN Z P， WU Y S， et al. Deviation control of unmanned aerial vehicles based on L1 method［J］. Journal of Projectiles， Rockets， Missiles and Guidance， 2021， 41（1）： 48-52 （in Chinese）. | |
| 86 | DONG S， JIAO Z X， SUN X H， et al. Dynamic allocation algorithm for the gain of UAV nose wheel steering and differential braking based on decomposition control［C］?∥2016 IEEE International Conference on Aircraft Utility Systems （AUS）. Piscataway： IEEE Press， 2016： 831-835. |
| 87 | KHATRI A， SINHA N. Aircraft maneuver design using bifurcation analysis and nonlinear control techniques［C］∥49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Reston：AIAA， 2011. |
| 88 | ZHANG M， LENG M， WU X. Design and analysis of all-electric aircraft nose wheel steering system based on intelligent algorithm?［C］?∥Proceedings of 2017 2nd International Conference on Applied Mechanics and Mechatronics Engineering（AMME 2017）. 2017. |
| 89 | ZHANG Y P， DUAN H B. A directional control system for UCAV automatic takeoff roll?［J］. Aircraft Engineering and Aerospace Technology， 2013， 85（1）： 48-61. |
| 90 | HUANG Z X， BEST M， KNOWLES J. Optimal predictive steering control for autonomous runway exits［J］. Advances in Mechanical Engineering， 2020， 12（12）： 1687814020980861. |
| 91 | 杨辉， 洪嘉振， 余征跃. 刚-柔耦合多体系统动力学建模与数值仿真［J］. 计算力学学报， 2003， 20（4）： 402-408. |
| YANG H， HONG J Z， YU Z Y. Dynamics modeling and numerical simulation for a rigid-flexible coup Ling multibody system［J］. Chinese Journal of Computational Mechanics， 2003， 20（4）： 402-408 （in Chinese）. | |
| 92 | 印寅， 聂宏， 魏小辉， 等. 多因素影响下的起落架收放系统性能分析［J］. 北京航空航天大学学报， 2015， 41（5）： 953-960. |
| YIN Y， NIE H， WEI X H， et al. Retraction system performance analysis of landing gear with the influence of multiple factors［J］. Journal of Beijing University of Aeronautics and Astronautics， 2015， 41（5）： 953-960 （in Chinese）. | |
| 93 | EARLES S W E， WU C L S. Motion analysis of a rigid-link mechanism with clearance at a bearing， using Lagrangian mechanics and digital computation［C］?∥Mechanisms 1972 Conference， 1973： 83-89. |
| 94 | WANG H X， NIE H. Performance analysis on retractable landing gear and design of ground test system［J］. Transactions of Nanjing University of Aeronautics and Astronautics， 2016， 33（6）： 670-677. |
| 95 | YIN Y， XU K， NIE H， et al. Dynamics analysis of spatial landing-gear mechanism with hinge clearance and axis deviation［J］. Journal of Aircraft， 2020， 58（1）： 30-42. |
| 96 | KNOWLES J A C， KRAUSKOPF B， LOWENBERG M H. Numerical continuation applied to landing gear mechanism analysis?［J］. Journal of Aircraft， 2011， 48（4）： 1254-1262. |
| 97 | YIN Y， NEILD S A， JIANG J Z， et al. Optimization of a main landing gear locking mechanism using bifurcation analysis［J］. Journal of Aircraft， 2017， 54（6）： 2126-2139. |
| 98 | KNOWLES J A C， KRAUSKOPF B， LOWENBERG M. Numerical continuation analysis of a three-dimensional aircraft main landing gear mechanism［J］. Nonlinear Dynamics， 2013， 71（1）： 331-352. |
| 99 | KNOWLES J A C， LOWENBERG M H， NEILD S A， et al. A bifurcation study to guide the design of a landing gear with a combined uplock/downlock mechanism?［J］. Proceedings Mathematical， Physical， and Engineering Sciences， 2014， 470（2172）： 20140332. |
| 100 | KNOWLES J A C. Bifurcation study of a dynamic model of a landing-gear mechanism?［J］. Journal of Aircraft， 2016， 53（5）： 1468-1477. |
| 101 | 杨易鑫， 印寅， 聂宏， 等. 基于分岔理论的起落架撑杆式锁机构设计［J］. 航空学报， 2020， 41（11）： 223958. |
| YANG Y X， YIN Y， NIE H， et al. Strut locking mechanism design for landing gear based on bifurcation theory［J］. Acta Aeronautica et Astronautica Sinica， 2020， 41（11）： 223958 （in Chinese）. | |
| 102 | KNOWLES J A C， KRAUSKOPF B， COETZEE E B. Unlocking a nose landing gear in different flight conditions： Folds， cusps and a swallowtail?［J］. Nonlinear Dynamics， 2021， 106（4）： 2943-2961. |
| 103 | KNOWLES J A C， KRAUSKOPF B， LOWENBERG M H， et al. Numerical continuation analysis of a dual-sidestay main landing gear mechanism［J］. Journal of Aircraft， 2014， 51（1）： 129-143. |
| 104 | XU K， YIN Y， YANG Y X， et al. Kinematic singularity and bifurcation analysis of sidestay landing gear locking mechanisms［J］. International Journal of Aerospace Engineering， 2021， 2021（1）： 6685635. |
| 105 | XU K， YIN Y， YANG Y X， et al. Bifurcation analysis of dual-sidestay landing gear locking performance considering joint clearance［J］. Chinese Journal of Aeronautics， 2022， 35（7）： 209-226. |
| 106 | ZHANG Z P， WU S X， ZHU H， et al. Analysis of the synchronized locking dynamic characteristics of a dual-sidestay main landing gear retraction mechanism?［J］. Aerospace， 2024， 11（5）： 356. |
| 107 | YIN Y， YANG Y X， XU K， et al. Bifurcation characteristics of emergency extension of a landing gear mechanism considering aerodynamic effect［J］. Journal of Aerospace Engineering， 2021， 34（5）： 04021046. |
| 108 | 徐奎. 双撑杆起落架收放动力学及锁定分岔特性研究［D］.南京：南京航空航天大学， 2021. |
| XU K. Dynamics and locking bifurcation analysis of retraction of dual-sidestay landing gear［D］. Nanjing：Nanjing University of Aeronautics and Astronautics， 2021 （in Chinese）. | |
| 109 | BUREAU E， SCHILDER F， FERREIRA SANTOS I， et al. Experimental bifurcation analysis of an impact oscillator： Tuning a non-invasive control scheme?［J］. Journal of Sound and Vibration， 2013， 332（22）： 5883-5897. |
| 110 | RENSON L， SHAW A D， BARTON D A W， et al. Application of control-based continuation to a nonlinear structure with harmonically coupled modes［J］. Mechanical Systems and Signal Processing， 2019， 120： 449-464. |
| 111 | LI Y Y， YIN Y， ZHANG Z P， et al. Control-based continuation methods for bifurcation characteristic study of landing gear strut locking mechanism?［C］?∥Advances in Automation， Mechanical and Design Engineering. Cham： Springer Nature Switzerland， 2024： 177-185. |
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