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Impact dynamics in biped locomotion analysis: Two modelling and implementation approaches
1. | University of La Réunion, Analyse et Ingénierie Mathématique AIM/LIM EA 2525, Parc Technologique Universitaire, Bâtiment 2, 2 rue Joseph Wetzell, 97490 Sainte-Clotilde, France |
2. | Robotics department, Mihajlo Pupin Institute, University of Belgrade, Zvezdara, Volgina 15, 11060 Belgrade, Serbia |
[1] |
Andaluzia Matei, Mircea Sofonea. Dual formulation of a viscoplastic contact problem with unilateral constraint. Discrete and Continuous Dynamical Systems - S, 2013, 6 (6) : 1587-1598. doi: 10.3934/dcdss.2013.6.1587 |
[2] |
Sebastián Ferrer, Francisco Crespo. Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems. Journal of Geometric Mechanics, 2014, 6 (4) : 479-502. doi: 10.3934/jgm.2014.6.479 |
[3] |
Felix X.-F. Ye, Hong Qian. Stochastic dynamics Ⅱ: Finite random dynamical systems, linear representation, and entropy production. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4341-4366. doi: 10.3934/dcdsb.2019122 |
[4] |
Mohamed Aly Tawhid. Nonsmooth generalized complementarity as unconstrained optimization. Journal of Industrial and Management Optimization, 2010, 6 (2) : 411-423. doi: 10.3934/jimo.2010.6.411 |
[5] |
Oanh Chau, R. Oujja, Mohamed Rochdi. A mathematical analysis of a dynamical frictional contact model in thermoviscoelasticity. Discrete and Continuous Dynamical Systems - S, 2008, 1 (1) : 61-70. doi: 10.3934/dcdss.2008.1.61 |
[6] |
Qihuai Liu, Pedro J. Torres. Orbital dynamics on invariant sets of contact Hamiltonian systems. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021297 |
[7] |
Zhisheng Shuai, P. van den Driessche. Impact of heterogeneity on the dynamics of an SEIR epidemic model. Mathematical Biosciences & Engineering, 2012, 9 (2) : 393-411. doi: 10.3934/mbe.2012.9.393 |
[8] |
Fengming Ma, Yiju Wang, Hongge Zhao. A potential reduction method for the generalized linear complementarity problem over a polyhedral cone. Journal of Industrial and Management Optimization, 2010, 6 (1) : 259-267. doi: 10.3934/jimo.2010.6.259 |
[9] |
Jie Zhang, Yue Wu, Liwei Zhang. A class of smoothing SAA methods for a stochastic linear complementarity problem. Numerical Algebra, Control and Optimization, 2012, 2 (1) : 145-156. doi: 10.3934/naco.2012.2.145 |
[10] |
Kari Astala, Jennifer L. Mueller, Lassi Päivärinta, Allan Perämäki, Samuli Siltanen. Direct electrical impedance tomography for nonsmooth conductivities. Inverse Problems and Imaging, 2011, 5 (3) : 531-549. doi: 10.3934/ipi.2011.5.531 |
[11] |
D. Motreanu, V. V. Motreanu, Nikolaos S. Papageorgiou. Nonautonomous resonant periodic systems with indefinite linear part and a nonsmooth potential. Communications on Pure and Applied Analysis, 2011, 10 (5) : 1401-1414. doi: 10.3934/cpaa.2011.10.1401 |
[12] |
Gilles Carbou, Bernard Hanouzet. Relaxation approximation of the Kerr model for the impedance initial-boundary value problem. Conference Publications, 2007, 2007 (Special) : 212-220. doi: 10.3934/proc.2007.2007.212 |
[13] |
Jianquan Li, Xiaoqin Wang, Xiaolin Lin. Impact of behavioral change on the epidemic characteristics of an epidemic model without vital dynamics. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1425-1434. doi: 10.3934/mbe.2018065 |
[14] |
Zhenyuan Guo, Lihong Huang, Xingfu Zou. Impact of discontinuous treatments on disease dynamics in an SIR epidemic model. Mathematical Biosciences & Engineering, 2012, 9 (1) : 97-110. doi: 10.3934/mbe.2012.9.97 |
[15] |
Martin Redmann, Melina A. Freitag. Balanced model order reduction for linear random dynamical systems driven by Lévy noise. Journal of Computational Dynamics, 2018, 5 (1&2) : 33-59. doi: 10.3934/jcd.2018002 |
[16] |
Huong Le Thi, Stéphane Junca, Mathias Legrand. First Return Time to the contact hyperplane for $ N $-degree-of-freedom vibro-impact systems. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 1-44. doi: 10.3934/dcdsb.2021031 |
[17] |
Ghendrih Philippe, Hauray Maxime, Anne Nouri. Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solution. Kinetic and Related Models, 2009, 2 (4) : 707-725. doi: 10.3934/krm.2009.2.707 |
[18] |
Yunan Wu, Guangya Chen, T. C. Edwin Cheng. A vector network equilibrium problem with a unilateral constraint. Journal of Industrial and Management Optimization, 2010, 6 (3) : 453-464. doi: 10.3934/jimo.2010.6.453 |
[19] |
Matthias Morzfeld, Daniel T. Kawano, Fai Ma. Characterization of damped linear dynamical systems in free motion. Numerical Algebra, Control and Optimization, 2013, 3 (1) : 49-62. doi: 10.3934/naco.2013.3.49 |
[20] |
Li-Xia Liu, Sanyang Liu, Chun-Feng Wang. Smoothing Newton methods for symmetric cone linear complementarity problem with the Cartesian $P$/$P_0$-property. Journal of Industrial and Management Optimization, 2011, 7 (1) : 53-66. doi: 10.3934/jimo.2011.7.53 |
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