Linear stability analysis of nonholonomic multibody systems
•Three procedures are illustrated to linearize the equations of nonholonomic systems.•Three nonholonomic systems are studied: a skateboard, a hoop and a torus.•The linear stability of these systems is analysed.•The values of the eigenvalues of the Jacobian matrices are discussed.•The characteristics...
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| Published in | International journal of mechanical sciences Vol. 198; p. 106392 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
15.05.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0020-7403 1879-2162 |
| DOI | 10.1016/j.ijmecsci.2021.106392 |
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| Abstract | •Three procedures are illustrated to linearize the equations of nonholonomic systems.•Three nonholonomic systems are studied: a skateboard, a hoop and a torus.•The linear stability of these systems is analysed.•The values of the eigenvalues of the Jacobian matrices are discussed.•The characteristics of the linearization approaches are summarized.
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This paper illustrates the application of three novel linearization procedures, recently validated with a well-acknowledged bicycle benchmark and valid for general multibody systems with holonomic and nonholonomic constraints, to study the linear stability of some examples of nonholonomic multibody systems. Despite the dynamics and control of mechanical systems with nonholonomic constraints have been widely researched and discussed, the linearization of their equations of motion and stability analyses along different types of trajectories are more uncharted subjects. In particular, the linear stability of the forward motion with constant velocity of three nonholonomic systems is analysed: a simplified skateboard model, similar to a Chaplygin sleigh; a hoop rolling without slipping, and a torus rolling without slipping. The nonlinear equations of motion of these systems are obtained by means of a multibody system dynamics approach. Three different procedures are used to perform the linearization of the equations of motion, leading to linear systems of different sizes. The values of the resulting eigenvalues are compared and discussed for each of the previously mentioned nonholonomic systems. |
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| AbstractList | •Three procedures are illustrated to linearize the equations of nonholonomic systems.•Three nonholonomic systems are studied: a skateboard, a hoop and a torus.•The linear stability of these systems is analysed.•The values of the eigenvalues of the Jacobian matrices are discussed.•The characteristics of the linearization approaches are summarized.
[Display omitted]
This paper illustrates the application of three novel linearization procedures, recently validated with a well-acknowledged bicycle benchmark and valid for general multibody systems with holonomic and nonholonomic constraints, to study the linear stability of some examples of nonholonomic multibody systems. Despite the dynamics and control of mechanical systems with nonholonomic constraints have been widely researched and discussed, the linearization of their equations of motion and stability analyses along different types of trajectories are more uncharted subjects. In particular, the linear stability of the forward motion with constant velocity of three nonholonomic systems is analysed: a simplified skateboard model, similar to a Chaplygin sleigh; a hoop rolling without slipping, and a torus rolling without slipping. The nonlinear equations of motion of these systems are obtained by means of a multibody system dynamics approach. Three different procedures are used to perform the linearization of the equations of motion, leading to linear systems of different sizes. The values of the resulting eigenvalues are compared and discussed for each of the previously mentioned nonholonomic systems. |
| ArticleNumber | 106392 |
| Author | García-Vallejo, D. Agúndez, A.G. Freire, E. |
| Author_xml | – sequence: 1 givenname: A.G. orcidid: 0000-0001-9638-0754 surname: Agúndez fullname: Agúndez, A.G. email: agarciaagundez@us.es organization: Departamento de Ingeniería Mecánica y Fabricación, Universidad de Sevilla, SPAIN – sequence: 2 givenname: D. orcidid: 0000-0002-2319-2688 surname: García-Vallejo fullname: García-Vallejo, D. organization: Departamento de Ingeniería Mecánica y Fabricación, Universidad de Sevilla, SPAIN – sequence: 3 givenname: E. surname: Freire fullname: Freire, E. organization: Departamento de Matemática Aplicada II, Universidad de Sevilla, SPAIN |
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| Cites_doi | 10.1109/87.572125 10.1177/02783640022066833 10.1007/BF00045108 10.1134/S1560354717080056 10.1016/j.mechmachtheory.2020.103826 10.3367/UFNe.0184.201405b.0493 10.1016/0034-4877(94)90038-8 10.1016/S0034-4877(98)80003-7 10.1016/S0167-2789(00)00046-4 10.1063/1.3559128 10.1007/s11044-007-9050-x 10.3934/dcdss.2010.3.85 10.1076/vesd.35.4.291.2042 10.1007/s11044-019-09707-y 10.1134/S1560354707030045 10.1007/s11071-020-06069-5 10.1023/A:1009745432698 10.1007/BF02199365 10.1070/PU2003v046n04ABEH001306 10.1016/S0034-4877(98)80006-2 10.1007/s10409-019-00914-6 10.1115/1.3424680 10.1109/TCST.2009.2034639 10.1109/70.88118 10.1007/s00419-020-01706-2 10.1137/S036301299223533X 10.1070/rd1999v004n02ABEH000105 10.1007/s11044-020-09741-1 10.1007/s11044-018-9626-7 10.1016/j.na.2008.01.037 10.1080/00423114.1999.12063093 10.1109/CDC.1990.203994 10.1109/37.476384 10.1109/9.277235 10.1023/A:1024575707338 10.1109/70.720345 10.1109/70.768190 10.1098/rspa.2007.1857 |
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| References | Schiehlen (bib0050) 1997; 1 Hubbard (bib0032) 1979; 46 Murray, Sastry (bib0008) 1993; 38 Kooijman, Schwab, Meijaard (bib0037) 2008; 19 Neimark, Fufaev (bib0001) 2004; vol. 33 Coleman, Holmes (bib0021) 1999; 4 Park, Yoo, Park, Choi (bib0013) 2009; 18 Arai, Tanie, Shiroma (bib0019) 1998; 14 Pappalardo, Lettieri, Guida (bib0048) 2020 Divelbiss, Wen (bib0012) 1997; 5 Sharp (bib0043) 2001; 35 Marsden J.E., Koon W.-S. The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems1996;. Ostrowski, Desai, Kumar (bib0025) 2000; 19 García-Agúndez, García-Vallejo, Freire (bib0040) 2020; 149 Shabana (bib0041) 2009 Samson (bib0014) 1992; vol. 13 Yang, Kim (bib0011) 1999; 15 Van der Schaft, Maschke (bib0002) 1994; 34 García-Agúndez, García-Vallejo, Freire (bib0049) 2021 Murray R.M., Sastry S.S. Steering nonholonomic systems in chained form1991;. Pomet, Thuilot, Bastin, Campion (bib0015) 1992 Escalona, Kłodowski, Munoz (bib0038) 2018; 43 Kremnev, Kuleshov (bib0033) 2010; 3 Bloch, Krishnaprasad, Marsden, Murray (bib0005) 1996; 136 Kuleshov (bib0026) 2007; 12 Cendra, Marsden, Ratiu (bib0007) 2001 Bloch, Crouch (bib0030) 1995; 33 Li, Canny (bib0031) 1990; 6 Ruina (bib0020) 1998; 42 González, Masarati, Cuadrado, Naya (bib0047) 2017; 12 Borisov, Kazakov, Kuznetsov (bib0035) 2014; 57 Han, Bauchau (bib0046) 2020 Bloch (bib0022) 2000; 141 Kolmanovsky, McClamroch (bib0018) 1995; 15 O’Reilly (bib0027) 1996; 10 Xiong, Wang, Liu (bib0045) 2020; 36 Müller, Schiehlen (bib0042) 2012; vol. 7 Borisov, Mamaev (bib0034) 2003; 46 Meijaard, Papadopoulos, Ruina, Schwab (bib0036) 2007; 463 Cantrijn, De León, Marrero, De Diego (bib0006) 1998; 42 Flannery (bib0004) 2011; 52 Xiong, Wang, Liu (bib0044) 2020; 48 Ostrowski, Lewis, Murray, Burdick (bib0024) 1994 Schwab, Meijaard (bib0028) 1999; 33 Bizyaev, Borisov, Mamaev (bib0023) 2017; 22 Bloch (bib0017) 2003 Laumond (bib0010) 1998; vol. 229 Zeng, Chen, Zhang, Guan (bib0039) 2018 Schwab, Meijaard (bib0029) 2003; 10 Zheng, Wu (bib0016) 2009; 70 García-Agúndez (10.1016/j.ijmecsci.2021.106392_bib0040) 2020; 149 Ruina (10.1016/j.ijmecsci.2021.106392_bib0020) 1998; 42 Ostrowski (10.1016/j.ijmecsci.2021.106392_bib0025) 2000; 19 Escalona (10.1016/j.ijmecsci.2021.106392_bib0038) 2018; 43 Pomet (10.1016/j.ijmecsci.2021.106392_bib0015) 1992 Kremnev (10.1016/j.ijmecsci.2021.106392_bib0033) 2010; 3 Sharp (10.1016/j.ijmecsci.2021.106392_bib0043) 2001; 35 González (10.1016/j.ijmecsci.2021.106392_bib0047) 2017; 12 Han (10.1016/j.ijmecsci.2021.106392_bib0046) 2020 Arai (10.1016/j.ijmecsci.2021.106392_bib0019) 1998; 14 Divelbiss (10.1016/j.ijmecsci.2021.106392_bib0012) 1997; 5 García-Agúndez (10.1016/j.ijmecsci.2021.106392_bib0049) 2021 Xiong (10.1016/j.ijmecsci.2021.106392_bib0045) 2020; 36 Schiehlen (10.1016/j.ijmecsci.2021.106392_bib0050) 1997; 1 Schwab (10.1016/j.ijmecsci.2021.106392_bib0029) 2003; 10 Xiong (10.1016/j.ijmecsci.2021.106392_bib0044) 2020; 48 Ostrowski (10.1016/j.ijmecsci.2021.106392_bib0024) 1994 Bizyaev (10.1016/j.ijmecsci.2021.106392_bib0023) 2017; 22 10.1016/j.ijmecsci.2021.106392_bib0009 Coleman (10.1016/j.ijmecsci.2021.106392_bib0021) 1999; 4 Borisov (10.1016/j.ijmecsci.2021.106392_bib0034) 2003; 46 Van der Schaft (10.1016/j.ijmecsci.2021.106392_bib0002) 1994; 34 Cantrijn (10.1016/j.ijmecsci.2021.106392_bib0006) 1998; 42 Cendra (10.1016/j.ijmecsci.2021.106392_bib0007) 2001 10.1016/j.ijmecsci.2021.106392_bib0003 Park (10.1016/j.ijmecsci.2021.106392_bib0013) 2009; 18 Zheng (10.1016/j.ijmecsci.2021.106392_bib0016) 2009; 70 Schwab (10.1016/j.ijmecsci.2021.106392_bib0028) 1999; 33 Murray (10.1016/j.ijmecsci.2021.106392_bib0008) 1993; 38 Meijaard (10.1016/j.ijmecsci.2021.106392_bib0036) 2007; 463 Kuleshov (10.1016/j.ijmecsci.2021.106392_bib0026) 2007; 12 Müller (10.1016/j.ijmecsci.2021.106392_bib0042) 2012; vol. 7 Bloch (10.1016/j.ijmecsci.2021.106392_bib0022) 2000; 141 Hubbard (10.1016/j.ijmecsci.2021.106392_bib0032) 1979; 46 Borisov (10.1016/j.ijmecsci.2021.106392_bib0035) 2014; 57 Bloch (10.1016/j.ijmecsci.2021.106392_bib0017) 2003 Li (10.1016/j.ijmecsci.2021.106392_bib0031) 1990; 6 Samson (10.1016/j.ijmecsci.2021.106392_sbref0014) 1992; vol. 13 Shabana (10.1016/j.ijmecsci.2021.106392_bib0041) 2009 Bloch (10.1016/j.ijmecsci.2021.106392_bib0005) 1996; 136 Kolmanovsky (10.1016/j.ijmecsci.2021.106392_bib0018) 1995; 15 Pappalardo (10.1016/j.ijmecsci.2021.106392_bib0048) 2020 O’Reilly (10.1016/j.ijmecsci.2021.106392_bib0027) 1996; 10 Laumond (10.1016/j.ijmecsci.2021.106392_bib0010) 1998; vol. 229 Flannery (10.1016/j.ijmecsci.2021.106392_bib0004) 2011; 52 Yang (10.1016/j.ijmecsci.2021.106392_bib0011) 1999; 15 Bloch (10.1016/j.ijmecsci.2021.106392_bib0030) 1995; 33 Kooijman (10.1016/j.ijmecsci.2021.106392_bib0037) 2008; 19 Zeng (10.1016/j.ijmecsci.2021.106392_bib0039) 2018 Neimark (10.1016/j.ijmecsci.2021.106392_bib0001) 2004; vol. 33 |
| References_xml | – volume: 136 start-page: 21 year: 1996 end-page: 99 ident: bib0005 article-title: Nonholonomic mechanical systems with symmetry publication-title: Arch Ration Mech Anal – volume: 57 start-page: 453 year: 2014 ident: bib0035 article-title: Nonlinear dynamics of the rattleback: a nonholonomic model publication-title: Phys Usp – volume: 33 start-page: 338 year: 1999 end-page: 349 ident: bib0028 article-title: Dynamics of flexible multibody systems having rolling contact: application of the wheel element to the dynamics of road vehicles publication-title: Veh Syst Dyn – year: 2021 ident: bib0049 article-title: Linearization approaches for general multibody systems validated through stability analysis of a benchmark bicycle model publication-title: Nonlinear Dyn – volume: 149 start-page: 103826 year: 2020 ident: bib0040 article-title: Study of the forward locomotion of a three-dimensional multibody model of a waveboard by inverse dynamics publication-title: Mech Mach Theory – volume: 46 start-page: 931 year: 1979 ident: bib0032 article-title: Mechanics of skate boards publication-title: J Appl Mech – volume: 70 start-page: 904 year: 2009 end-page: 920 ident: bib0016 article-title: Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts publication-title: Nonlinear Analysis: Theory, Methods & Applications – year: 2009 ident: bib0041 article-title: Computational dynamics – volume: 5 start-page: 269 year: 1997 end-page: 278 ident: bib0012 article-title: Trajectory tracking control of a car-trailer system publication-title: IEEE Trans Control Syst Technol – volume: 33 start-page: 126 year: 1995 end-page: 148 ident: bib0030 article-title: Nonholonomic control systems on riemannian manifolds publication-title: SIAM J Control Optim – volume: 4 start-page: 55 year: 1999 end-page: 77 ident: bib0021 article-title: Motions and stability of a piecewise holonomic system: the discrete chaplygin sleigh publication-title: Regular and chaotic dynamics – volume: vol. 229 year: 1998 ident: bib0010 article-title: Robot motion planning and control – volume: vol. 7 year: 2012 ident: bib0042 article-title: Linear vibrations: a theoretical treatment of multi-degree-of-freedom vibrating systems – volume: 19 start-page: 115 year: 2008 end-page: 132 ident: bib0037 article-title: Experimental validation of a model of an uncontrolled bicycle publication-title: Multibody Syst Dyn – volume: 15 start-page: 578 year: 1999 end-page: 587 ident: bib0011 article-title: Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots publication-title: IEEE Transactions on robotics and automation – volume: vol. 33 year: 2004 ident: bib0001 article-title: Dynamics of nonholonomic systems – start-page: 1371 year: 2018 end-page: 1376 ident: bib0039 article-title: Kinematic modelling and analysis of an ess-board-like robot publication-title: 2018 IEEE International Conference on Robotics and Biomimetics (ROBIO) – volume: 38 start-page: 700 year: 1993 end-page: 716 ident: bib0008 article-title: Nonholonomic motion planning: steering using sinusoids publication-title: IEEE Trans Automat Contr – start-page: 2391 year: 1994 end-page: 2397 ident: bib0024 article-title: Nonholonomic mechanics and locomotion: the snakeboard example publication-title: Proceedings of the 1994 IEEE International Conference on Robotics and Automation – volume: 35 start-page: 291 year: 2001 end-page: 318 ident: bib0043 article-title: Stability, control and steering responses of motorcycles publication-title: Veh Syst Dyn – year: 2020 ident: bib0046 article-title: Simulation and stability analysis of periodic flexible multibody systems publication-title: Multibody Syst Dyn – volume: 12 year: 2017 ident: bib0047 article-title: Assessment of linearization approaches for multibody dynamics formulations publication-title: J Comput Nonlinear Dyn – volume: 19 start-page: 225 year: 2000 end-page: 237 ident: bib0025 article-title: Optimal gait selection for nonholonomic locomotion systems publication-title: Int J Rob Res – volume: 15 start-page: 20 year: 1995 end-page: 36 ident: bib0018 article-title: Developments in nonholonomic control problems publication-title: IEEE Control Syst Mag – volume: 10 start-page: 107 year: 2003 end-page: 123 ident: bib0029 article-title: Dynamics of flexible multibody systems with non-holonomic constraints: a finite element approach publication-title: Multibody Syst Dyn – start-page: 129 year: 1992 end-page: 134 ident: bib0015 article-title: A hybrid strategy for the feedback stabilization of nonholonomic mobile robots publication-title: Proceedings 1992 IEEE International Conference on Robotics and Automation – volume: vol. 13 year: 1992 ident: bib0014 article-title: Path following and time-varying feedback stabilization of a wheeled mobile robot publication-title: Proceedings of the international conference on advanced robotics and computer vision – volume: 42 start-page: 25 year: 1998 end-page: 45 ident: bib0006 article-title: Reduction of nonholonomic mechanical systems with symmetries publication-title: Rep Math Phys – year: 2020 ident: bib0048 article-title: Stability analysis of rigid multibody mechanical systems with holonomic and nonholonomic constraints publication-title: Archive of Applied Mechanics – volume: 52 start-page: 032705 year: 2011 ident: bib0004 article-title: D’Alembert–lagrange analytical dynamics for nonholonomic systems publication-title: J Math Phys – volume: 3 start-page: 85 year: 2010 ident: bib0033 article-title: Nonlinear dynamics and stability of the skateboard publication-title: Discrete & Continuous Dynamical Systems-S – volume: 36 start-page: 220 year: 2020 end-page: 233 ident: bib0045 article-title: Bicycle dynamics and its circular solution on a revolution surface publication-title: Acta Mech Sin – volume: 1 start-page: 149 year: 1997 end-page: 188 ident: bib0050 article-title: Multibody system dynamics: roots and perspectives publication-title: Multibody Syst Dyn – volume: 18 start-page: 1199 year: 2009 end-page: 1206 ident: bib0013 article-title: A simple adaptive control approach for trajectory tracking of electrically driven nonholonomic mobile robots publication-title: IEEE Trans Control Syst Technol – start-page: 207 year: 2003 end-page: 276 ident: bib0017 article-title: Nonholonomic mechanics publication-title: Nonholonomic mechanics and control – volume: 42 start-page: 91 year: 1998 end-page: 100 ident: bib0020 article-title: Nonholonomic stability aspects of piecewise holonomic systems publication-title: Rep Math Phys – volume: 22 start-page: 955 year: 2017 end-page: 975 ident: bib0023 article-title: The chaplygin sleigh with parametric excitation: chaotic dynamics and nonholonomic acceleration publication-title: Regular and Chaotic Dynamics – volume: 141 start-page: 297 year: 2000 end-page: 315 ident: bib0022 article-title: Asymptotic hamiltonian dynamics: the toda lattice, the three-wave interaction and the non-holonomic chaplygin sleigh publication-title: Physica D – volume: 14 start-page: 681 year: 1998 end-page: 695 ident: bib0019 article-title: Nonholonomic control of a three-DOF planar underactuated manipulator publication-title: IEEE Transactions on Robotics and Automation – volume: 46 start-page: 393 year: 2003 ident: bib0034 article-title: Strange attractors in rattleback dynamics publication-title: Phys Usp – volume: 12 start-page: 321 year: 2007 end-page: 334 ident: bib0026 article-title: Further development of the mathematical model of a snakeboard publication-title: Regular and Chaotic Dynamics – volume: 48 start-page: 311 year: 2020 end-page: 335 ident: bib0044 article-title: Stability analysis for the whipple bicycle dynamics publication-title: Multibody Syst Dyn – start-page: 221 year: 2001 end-page: 273 ident: bib0007 article-title: Geometric mechanics, lagrangian reduction, and nonholonomic systems publication-title: Mathematics unlimited-2001 and beyond – reference: Murray R.M., Sastry S.S. Steering nonholonomic systems in chained form1991;. – volume: 10 start-page: 287 year: 1996 end-page: 305 ident: bib0027 article-title: The dynamies of rolling disks and sliding disks publication-title: Nonlinear Dyn – volume: 34 start-page: 225 year: 1994 end-page: 233 ident: bib0002 article-title: On the hamiltonian formulation of nonholonomic mechanical systems publication-title: Rep Math Phys – reference: Marsden J.E., Koon W.-S. The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems1996;. – volume: 463 start-page: 1955 year: 2007 end-page: 1982 ident: bib0036 article-title: Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review publication-title: Proceedings of the Royal society A: mathematical, physical and engineering sciences – volume: 43 start-page: 297 year: 2018 end-page: 319 ident: bib0038 article-title: Validation of multibody modeling and simulation using an instrumented bicycle: from the computer to the road publication-title: Multibody Syst Dyn – volume: 6 start-page: 62 year: 1990 end-page: 72 ident: bib0031 article-title: Motion of two rigid bodies with rolling constraint publication-title: IEEE Transactions on Robotics and Automation – volume: 5 start-page: 269 issue: 3 year: 1997 ident: 10.1016/j.ijmecsci.2021.106392_bib0012 article-title: Trajectory tracking control of a car-trailer system publication-title: IEEE Trans Control Syst Technol doi: 10.1109/87.572125 – volume: 19 start-page: 225 issue: 3 year: 2000 ident: 10.1016/j.ijmecsci.2021.106392_bib0025 article-title: Optimal gait selection for nonholonomic locomotion systems publication-title: Int J Rob Res doi: 10.1177/02783640022066833 – volume: 10 start-page: 287 issue: 3 year: 1996 ident: 10.1016/j.ijmecsci.2021.106392_bib0027 article-title: The dynamies of rolling disks and sliding disks publication-title: Nonlinear Dyn doi: 10.1007/BF00045108 – volume: vol. 13 year: 1992 ident: 10.1016/j.ijmecsci.2021.106392_sbref0014 article-title: Path following and time-varying feedback stabilization of a wheeled mobile robot – volume: 22 start-page: 955 issue: 8 year: 2017 ident: 10.1016/j.ijmecsci.2021.106392_bib0023 article-title: The chaplygin sleigh with parametric excitation: chaotic dynamics and nonholonomic acceleration publication-title: Regular and Chaotic Dynamics doi: 10.1134/S1560354717080056 – volume: 149 start-page: 103826 year: 2020 ident: 10.1016/j.ijmecsci.2021.106392_bib0040 article-title: Study of the forward locomotion of a three-dimensional multibody model of a waveboard by inverse dynamics publication-title: Mech Mach Theory doi: 10.1016/j.mechmachtheory.2020.103826 – volume: 12 issue: 4 year: 2017 ident: 10.1016/j.ijmecsci.2021.106392_bib0047 article-title: Assessment of linearization approaches for multibody dynamics formulations publication-title: J Comput Nonlinear Dyn – volume: 57 start-page: 453 issue: 5 year: 2014 ident: 10.1016/j.ijmecsci.2021.106392_bib0035 article-title: Nonlinear dynamics of the rattleback: a nonholonomic model publication-title: Phys Usp doi: 10.3367/UFNe.0184.201405b.0493 – volume: 34 start-page: 225 issue: 2 year: 1994 ident: 10.1016/j.ijmecsci.2021.106392_bib0002 article-title: On the hamiltonian formulation of nonholonomic mechanical systems publication-title: Rep Math Phys doi: 10.1016/0034-4877(94)90038-8 – volume: 42 start-page: 25 issue: 1–2 year: 1998 ident: 10.1016/j.ijmecsci.2021.106392_bib0006 article-title: Reduction of nonholonomic mechanical systems with symmetries publication-title: Rep Math Phys doi: 10.1016/S0034-4877(98)80003-7 – volume: 141 start-page: 297 issue: 3–4 year: 2000 ident: 10.1016/j.ijmecsci.2021.106392_bib0022 article-title: Asymptotic hamiltonian dynamics: the toda lattice, the three-wave interaction and the non-holonomic chaplygin sleigh publication-title: Physica D doi: 10.1016/S0167-2789(00)00046-4 – start-page: 1371 year: 2018 ident: 10.1016/j.ijmecsci.2021.106392_bib0039 article-title: Kinematic modelling and analysis of an ess-board-like robot – volume: 52 start-page: 032705 issue: 3 year: 2011 ident: 10.1016/j.ijmecsci.2021.106392_bib0004 article-title: D’Alembert–lagrange analytical dynamics for nonholonomic systems publication-title: J Math Phys doi: 10.1063/1.3559128 – volume: 19 start-page: 115 issue: 1–2 year: 2008 ident: 10.1016/j.ijmecsci.2021.106392_bib0037 article-title: Experimental validation of a model of an uncontrolled bicycle publication-title: Multibody Syst Dyn doi: 10.1007/s11044-007-9050-x – start-page: 2391 year: 1994 ident: 10.1016/j.ijmecsci.2021.106392_bib0024 article-title: Nonholonomic mechanics and locomotion: the snakeboard example – volume: 3 start-page: 85 issue: 1 year: 2010 ident: 10.1016/j.ijmecsci.2021.106392_bib0033 article-title: Nonlinear dynamics and stability of the skateboard publication-title: Discrete & Continuous Dynamical Systems-S doi: 10.3934/dcdss.2010.3.85 – volume: 35 start-page: 291 issue: 4–5 year: 2001 ident: 10.1016/j.ijmecsci.2021.106392_bib0043 article-title: Stability, control and steering responses of motorcycles publication-title: Veh Syst Dyn doi: 10.1076/vesd.35.4.291.2042 – volume: 48 start-page: 311 issue: 3 year: 2020 ident: 10.1016/j.ijmecsci.2021.106392_bib0044 article-title: Stability analysis for the whipple bicycle dynamics publication-title: Multibody Syst Dyn doi: 10.1007/s11044-019-09707-y – volume: 12 start-page: 321 issue: 3 year: 2007 ident: 10.1016/j.ijmecsci.2021.106392_bib0026 article-title: Further development of the mathematical model of a snakeboard publication-title: Regular and Chaotic Dynamics doi: 10.1134/S1560354707030045 – volume: vol. 229 year: 1998 ident: 10.1016/j.ijmecsci.2021.106392_bib0010 – year: 2009 ident: 10.1016/j.ijmecsci.2021.106392_bib0041 – year: 2021 ident: 10.1016/j.ijmecsci.2021.106392_bib0049 article-title: Linearization approaches for general multibody systems validated through stability analysis of a benchmark bicycle model publication-title: Nonlinear Dyn doi: 10.1007/s11071-020-06069-5 – volume: 1 start-page: 149 issue: 2 year: 1997 ident: 10.1016/j.ijmecsci.2021.106392_bib0050 article-title: Multibody system dynamics: roots and perspectives publication-title: Multibody Syst Dyn doi: 10.1023/A:1009745432698 – volume: 136 start-page: 21 issue: 1 year: 1996 ident: 10.1016/j.ijmecsci.2021.106392_bib0005 article-title: Nonholonomic mechanical systems with symmetry publication-title: Arch Ration Mech Anal doi: 10.1007/BF02199365 – volume: 46 start-page: 393 issue: 4 year: 2003 ident: 10.1016/j.ijmecsci.2021.106392_bib0034 article-title: Strange attractors in rattleback dynamics publication-title: Phys Usp doi: 10.1070/PU2003v046n04ABEH001306 – volume: 42 start-page: 91 issue: 1–2 year: 1998 ident: 10.1016/j.ijmecsci.2021.106392_bib0020 article-title: Nonholonomic stability aspects of piecewise holonomic systems publication-title: Rep Math Phys doi: 10.1016/S0034-4877(98)80006-2 – volume: 36 start-page: 220 issue: 1 year: 2020 ident: 10.1016/j.ijmecsci.2021.106392_bib0045 article-title: Bicycle dynamics and its circular solution on a revolution surface publication-title: Acta Mech Sin doi: 10.1007/s10409-019-00914-6 – volume: 46 start-page: 931 year: 1979 ident: 10.1016/j.ijmecsci.2021.106392_bib0032 article-title: Mechanics of skate boards publication-title: J Appl Mech doi: 10.1115/1.3424680 – volume: 18 start-page: 1199 issue: 5 year: 2009 ident: 10.1016/j.ijmecsci.2021.106392_bib0013 article-title: A simple adaptive control approach for trajectory tracking of electrically driven nonholonomic mobile robots publication-title: IEEE Trans Control Syst Technol doi: 10.1109/TCST.2009.2034639 – volume: vol. 33 year: 2004 ident: 10.1016/j.ijmecsci.2021.106392_bib0001 – ident: 10.1016/j.ijmecsci.2021.106392_bib0003 – volume: 6 start-page: 62 issue: 1 year: 1990 ident: 10.1016/j.ijmecsci.2021.106392_bib0031 article-title: Motion of two rigid bodies with rolling constraint publication-title: IEEE Transactions on Robotics and Automation doi: 10.1109/70.88118 – year: 2020 ident: 10.1016/j.ijmecsci.2021.106392_bib0048 article-title: Stability analysis of rigid multibody mechanical systems with holonomic and nonholonomic constraints publication-title: Archive of Applied Mechanics doi: 10.1007/s00419-020-01706-2 – volume: 33 start-page: 126 issue: 1 year: 1995 ident: 10.1016/j.ijmecsci.2021.106392_bib0030 article-title: Nonholonomic control systems on riemannian manifolds publication-title: SIAM J Control Optim doi: 10.1137/S036301299223533X – volume: 4 start-page: 55 issue: 2 year: 1999 ident: 10.1016/j.ijmecsci.2021.106392_bib0021 article-title: Motions and stability of a piecewise holonomic system: the discrete chaplygin sleigh publication-title: Regular and chaotic dynamics doi: 10.1070/rd1999v004n02ABEH000105 – start-page: 129 year: 1992 ident: 10.1016/j.ijmecsci.2021.106392_bib0015 article-title: A hybrid strategy for the feedback stabilization of nonholonomic mobile robots – year: 2020 ident: 10.1016/j.ijmecsci.2021.106392_bib0046 article-title: Simulation and stability analysis of periodic flexible multibody systems publication-title: Multibody Syst Dyn doi: 10.1007/s11044-020-09741-1 – volume: 43 start-page: 297 issue: 4 year: 2018 ident: 10.1016/j.ijmecsci.2021.106392_bib0038 article-title: Validation of multibody modeling and simulation using an instrumented bicycle: from the computer to the road publication-title: Multibody Syst Dyn doi: 10.1007/s11044-018-9626-7 – volume: 70 start-page: 904 issue: 2 year: 2009 ident: 10.1016/j.ijmecsci.2021.106392_bib0016 article-title: Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts publication-title: Nonlinear Analysis: Theory, Methods & Applications doi: 10.1016/j.na.2008.01.037 – volume: 33 start-page: 338 issue: sup1 year: 1999 ident: 10.1016/j.ijmecsci.2021.106392_bib0028 article-title: Dynamics of flexible multibody systems having rolling contact: application of the wheel element to the dynamics of road vehicles publication-title: Veh Syst Dyn doi: 10.1080/00423114.1999.12063093 – ident: 10.1016/j.ijmecsci.2021.106392_bib0009 doi: 10.1109/CDC.1990.203994 – volume: 15 start-page: 20 issue: 6 year: 1995 ident: 10.1016/j.ijmecsci.2021.106392_bib0018 article-title: Developments in nonholonomic control problems publication-title: IEEE Control Syst Mag doi: 10.1109/37.476384 – volume: vol. 7 year: 2012 ident: 10.1016/j.ijmecsci.2021.106392_bib0042 – volume: 38 start-page: 700 issue: 5 year: 1993 ident: 10.1016/j.ijmecsci.2021.106392_bib0008 article-title: Nonholonomic motion planning: steering using sinusoids publication-title: IEEE Trans Automat Contr doi: 10.1109/9.277235 – start-page: 207 year: 2003 ident: 10.1016/j.ijmecsci.2021.106392_bib0017 article-title: Nonholonomic mechanics – volume: 10 start-page: 107 issue: 1 year: 2003 ident: 10.1016/j.ijmecsci.2021.106392_bib0029 article-title: Dynamics of flexible multibody systems with non-holonomic constraints: a finite element approach publication-title: Multibody Syst Dyn doi: 10.1023/A:1024575707338 – volume: 14 start-page: 681 issue: 5 year: 1998 ident: 10.1016/j.ijmecsci.2021.106392_bib0019 article-title: Nonholonomic control of a three-DOF planar underactuated manipulator publication-title: IEEE Transactions on Robotics and Automation doi: 10.1109/70.720345 – start-page: 221 year: 2001 ident: 10.1016/j.ijmecsci.2021.106392_bib0007 article-title: Geometric mechanics, lagrangian reduction, and nonholonomic systems – volume: 15 start-page: 578 issue: 3 year: 1999 ident: 10.1016/j.ijmecsci.2021.106392_bib0011 article-title: Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots publication-title: IEEE Transactions on robotics and automation doi: 10.1109/70.768190 – volume: 463 start-page: 1955 issue: 2084 year: 2007 ident: 10.1016/j.ijmecsci.2021.106392_bib0036 article-title: Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review publication-title: Proceedings of the Royal society A: mathematical, physical and engineering sciences doi: 10.1098/rspa.2007.1857 |
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| Snippet | •Three procedures are illustrated to linearize the equations of nonholonomic systems.•Three nonholonomic systems are studied: a skateboard, a hoop and a... |
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| Title | Linear stability analysis of nonholonomic multibody systems |
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