Edit Profile (opens in new tab) Nordmark, Arne B. Co-Author Distance Author ID: nordmark.arne-b Published as: Nordmark, Arne; Nordmark, Arne B.; Nordmark, A.; Nordmark, A. B. more...less Documents Indexed: 39 Publications since 1992 Co-Authors: 22 Co-Authors with 36 Joint Publications 641 Co-Co-Authors all top 5 Co-Authors 3 single-authored 8 Essén, Hanno 7 Eriksson, Anders B. 7 Kowalczyk, Piotr 6 Dankowicz, Harry J. 5 Champneys, Alan R. 5 di Bernardo, Mario 5 Piiroinen, Petri T. 3 Fredriksson, Mats H. 2 Glendinning, Paul Alexander 1 Adolfsson, Jesper 1 Borglund, Dan 1 Budd, Christopher John 1 Chillingworth, D. R. J. 1 Hogan, S. John 1 Homer, Martin E. 1 Kuznetsov, Yuri Alexandrovich 1 Lindborg, Erik 1 Olivar, Gerard 1 Patil, Amit 1 Pettersson, Robert 1 Tost, Gerard Olivar 1 Várkonyi, Péter László all top 5 Serials 7 European Journal of Physics 3 Nonlinearity 3 Physica D 3 Computational Mechanics 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Nonlinear Dynamics 2 Computer Methods in Applied Mechanics and Engineering 2 IMA Journal of Applied Mathematics 2 Multibody System Dynamics 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 International Journal of Non-Linear Mechanics 1 Journal of Fluid Mechanics 1 Chaos, Solitons and Fractals 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Review 1 European Journal of Mechanics. A. Solids 1 Dynamical Systems 1 SIAM Journal on Applied Dynamical Systems all top 5 Fields 23 Mechanics of particles and systems (70-XX) 12 Dynamical systems and ergodic theory (37-XX) 10 Ordinary differential equations (34-XX) 8 Mechanics of deformable solids (74-XX) 2 Biology and other natural sciences (92-XX) 1 Partial differential equations (35-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 36 Publications have been cited 735 times in 485 Documents Cited by ▼ Year ▼ Bifurcations in nonsmooth dynamical systems. Zbl 1168.34006 di Bernardo, Mario; Budd, Chris J.; Champneys, Alan R.; Kowalczyk, Piotr; Nordmark, Arne B.; Tost, Gerard Olivar; Piiroinen, Petri T. 153 2008 On the origin and bifurcations of stick-slip oscillations. Zbl 0963.70016 Dankowicz, Harry; Nordmark, Arne B. 81 2000 Bifurcations of dynamical systems with sliding: derivation of normal-form mappings. Zbl 1008.37029 di Bernardo, M.; Kowalczyk, P.; Nordmark, A. 80 2002 Sliding bifurcations: a novel mechanism for the sudden onset of chaos in dry friction oscillators. Zbl 1099.70504 di Bernardo, M.; Kowalczyk, P.; Nordmark, A. 75 2003 Discontinuity-induced bifurcations of equilibria in piecewise-smooth and impacting dynamical systems. Zbl 1170.34027 di Bernardo, M.; Nordmark, A.; Olivar, G. 35 2008 Bifurcations caused by grazing incidence in many degrees of freedom impact oscillators. Zbl 0887.70016 Fredriksson, Mats H.; Nordmark, Arne B. 33 1997 On normal form calculations in impact oscillators. Zbl 0968.34008 Fredriksson, Mats H.; Nordmark, Arne B. 32 2000 Two-parameter discontinuity-induced bifurcations of limit cycles: classification and open problems. Zbl 1141.37341 Kowalczyk, P.; Di Bernardo, M.; Champneys, A. R.; Hogan, S. J.; Homer, M.; Piiroinen, P. T.; Kuznetsov, Yu. A.; Nordmark, A. 30 2006 Existence of periodic orbits in grazing bifurcations of impacting mechanical oscillators. Zbl 1001.70020 Nordmark, Arne B. 27 2001 Simulation and stability analysis of impacting systems with complete chattering. Zbl 1183.70038 Nordmark, Arne B.; Piiroinen, Petri T. 23 2009 Low-velocity impacts of quasiperiodic oscillations. Zbl 1162.70325 Dankowicz, Harry; Piiroinen, Petri; Nordmark, Arne B. 22 2002 Effects due to low velocity impact in mechanical oscillators. Zbl 0900.70304 Nordmark, A. B. 20 1992 A codimension-two scenario of sliding solutions in grazing-sliding bifurcations. Zbl 1102.37034 Nordmark, A. B.; Kowalczyk, P. 15 2006 Discontinuity-induced bifurcations in systems with impacts and friction: discontinuities in the impact law. Zbl 1203.70027 Nordmark, Arne; Dankowicz, Harry; Champneys, Alan 14 2009 Friction-induced reverse chatter in rigid-body mechanisms with impacts. Zbl 1385.70030 Nordmark, Arne; Dankowicz, Harry; Champneys, Alan 14 2011 Instability of hyper-elastic balloon-shaped space membranes under pressure loads. Zbl 1253.74050 Eriksson, Anders; Nordmark, Arne 12 2012 3D passive walkers: Finding periodic gaits in the presence of discontinuities. Zbl 0987.70007 Adolfsson, Jesper; Dankowicz, Harry; Nordmark, Arne 11 2001 Attractors near grazing-sliding bifurcations. Zbl 1246.34019 Glendinning, P.; Kowalczyk, P.; Nordmark, A. B. 10 2012 Multiple attractors in grazing-sliding bifurcations in Filippov-type flows. Zbl 1404.37059 Glendinning, Paul; Kowalczyk, Piotr; Nordmark, Arne B. 7 2016 Discontinuity mappings for vector fields with higher order continuity. Zbl 1032.37009 Nordmark, Arne B. 5 2002 Breaking symmetries and constraints: Transitions from 2D to 3D in passive walkers. Zbl 1072.70004 Piiroinen, Petri T.; Dankowicz, Harry J.; Nordmark, Arne B. 5 2003 Experiments on the onset of impacting motion using a pipe conveying fluid. Zbl 0965.70003 Fredriksson, Mats H.; Borglund, Dan; Nordmark, Arne B. 4 1999 Two-dimensional turbulence on a sphere. Zbl 1511.76041 Lindborg, Erik; Nordmark, Arne 4 2022 Temporal finite element formulation of optimal control in mechanisms. Zbl 1231.70001 Eriksson, Anders; Nordmark, Arne 3 2010 Symmetry aspects in stability investigations for thin membranes. Zbl 1398.74202 Eriksson, Anders; Nordmark, Arne 3 2016 Wrinkling of cylindrical membranes with non-uniform thickness. Zbl 1406.74422 Patil, Amit; Nordmark, Arne; Eriksson, Anders 3 2015 Dynamics beyond dynamic jam; unfolding the Painlevé paradox singularity. Zbl 1393.70032 Nordmark, Arne; Várkonyi, Peter L.; Champneys, Alan R. 3 2018 Systems with a preferred spin direction. Zbl 0930.70014 Nordmark, A.; Essén, Hanno 2 1999 The comfortable roller coaster-on the shape of tracks with a constant normal force. Zbl 1202.70117 Nordmark, Arne B.; Essén, Hanno 2 2010 The skipping rope curve. Zbl 1128.70309 Nordmark, Arne; Essén, Hanno 1 2007 Static deformation of a heavy spring due to gravity and centrifugal force. Zbl 1423.74335 Essén, Hanno; Nordmark, Arne 1 2010 An impacting linear three body system. Zbl 1390.70018 Nordmark, Arne; Essén, Hanno 1 2018 Relativistic version of the Feynman-Dyson-Hughes derivation of the Lorentz force law and Maxwell’s homogeneous equations. Zbl 1349.78013 Essén, Hanno; Nordmark, Arne B. 1 2016 Periodic orbits close to grazing for an impact oscillator. Zbl 1314.34087 Chillingworth, D. R. J.; Nordmark, A. B. 1 2013 Constrained stability of conservative static equilibrium. Zbl 1470.74028 Eriksson, Anders; Nordmark, Arne 1 2019 Computational stability investigations for a highly symmetric system: the pressurized spherical membrane. Zbl 1464.74055 Eriksson, Anders; Nordmark, Arne 1 2020 Two-dimensional turbulence on a sphere. Zbl 1511.76041 Lindborg, Erik; Nordmark, Arne 4 2022 Computational stability investigations for a highly symmetric system: the pressurized spherical membrane. Zbl 1464.74055 Eriksson, Anders; Nordmark, Arne 1 2020 Constrained stability of conservative static equilibrium. Zbl 1470.74028 Eriksson, Anders; Nordmark, Arne 1 2019 Dynamics beyond dynamic jam; unfolding the Painlevé paradox singularity. Zbl 1393.70032 Nordmark, Arne; Várkonyi, Peter L.; Champneys, Alan R. 3 2018 An impacting linear three body system. Zbl 1390.70018 Nordmark, Arne; Essén, Hanno 1 2018 Multiple attractors in grazing-sliding bifurcations in Filippov-type flows. Zbl 1404.37059 Glendinning, Paul; Kowalczyk, Piotr; Nordmark, Arne B. 7 2016 Symmetry aspects in stability investigations for thin membranes. Zbl 1398.74202 Eriksson, Anders; Nordmark, Arne 3 2016 Relativistic version of the Feynman-Dyson-Hughes derivation of the Lorentz force law and Maxwell’s homogeneous equations. Zbl 1349.78013 Essén, Hanno; Nordmark, Arne B. 1 2016 Wrinkling of cylindrical membranes with non-uniform thickness. Zbl 1406.74422 Patil, Amit; Nordmark, Arne; Eriksson, Anders 3 2015 Periodic orbits close to grazing for an impact oscillator. Zbl 1314.34087 Chillingworth, D. R. J.; Nordmark, A. B. 1 2013 Instability of hyper-elastic balloon-shaped space membranes under pressure loads. Zbl 1253.74050 Eriksson, Anders; Nordmark, Arne 12 2012 Attractors near grazing-sliding bifurcations. Zbl 1246.34019 Glendinning, P.; Kowalczyk, P.; Nordmark, A. B. 10 2012 Friction-induced reverse chatter in rigid-body mechanisms with impacts. Zbl 1385.70030 Nordmark, Arne; Dankowicz, Harry; Champneys, Alan 14 2011 Temporal finite element formulation of optimal control in mechanisms. Zbl 1231.70001 Eriksson, Anders; Nordmark, Arne 3 2010 The comfortable roller coaster-on the shape of tracks with a constant normal force. Zbl 1202.70117 Nordmark, Arne B.; Essén, Hanno 2 2010 Static deformation of a heavy spring due to gravity and centrifugal force. Zbl 1423.74335 Essén, Hanno; Nordmark, Arne 1 2010 Simulation and stability analysis of impacting systems with complete chattering. Zbl 1183.70038 Nordmark, Arne B.; Piiroinen, Petri T. 23 2009 Discontinuity-induced bifurcations in systems with impacts and friction: discontinuities in the impact law. Zbl 1203.70027 Nordmark, Arne; Dankowicz, Harry; Champneys, Alan 14 2009 Bifurcations in nonsmooth dynamical systems. Zbl 1168.34006 di Bernardo, Mario; Budd, Chris J.; Champneys, Alan R.; Kowalczyk, Piotr; Nordmark, Arne B.; Tost, Gerard Olivar; Piiroinen, Petri T. 153 2008 Discontinuity-induced bifurcations of equilibria in piecewise-smooth and impacting dynamical systems. Zbl 1170.34027 di Bernardo, M.; Nordmark, A.; Olivar, G. 35 2008 The skipping rope curve. Zbl 1128.70309 Nordmark, Arne; Essén, Hanno 1 2007 Two-parameter discontinuity-induced bifurcations of limit cycles: classification and open problems. Zbl 1141.37341 Kowalczyk, P.; Di Bernardo, M.; Champneys, A. R.; Hogan, S. J.; Homer, M.; Piiroinen, P. T.; Kuznetsov, Yu. A.; Nordmark, A. 30 2006 A codimension-two scenario of sliding solutions in grazing-sliding bifurcations. Zbl 1102.37034 Nordmark, A. B.; Kowalczyk, P. 15 2006 Sliding bifurcations: a novel mechanism for the sudden onset of chaos in dry friction oscillators. Zbl 1099.70504 di Bernardo, M.; Kowalczyk, P.; Nordmark, A. 75 2003 Breaking symmetries and constraints: Transitions from 2D to 3D in passive walkers. Zbl 1072.70004 Piiroinen, Petri T.; Dankowicz, Harry J.; Nordmark, Arne B. 5 2003 Bifurcations of dynamical systems with sliding: derivation of normal-form mappings. Zbl 1008.37029 di Bernardo, M.; Kowalczyk, P.; Nordmark, A. 80 2002 Low-velocity impacts of quasiperiodic oscillations. Zbl 1162.70325 Dankowicz, Harry; Piiroinen, Petri; Nordmark, Arne B. 22 2002 Discontinuity mappings for vector fields with higher order continuity. Zbl 1032.37009 Nordmark, Arne B. 5 2002 Existence of periodic orbits in grazing bifurcations of impacting mechanical oscillators. Zbl 1001.70020 Nordmark, Arne B. 27 2001 3D passive walkers: Finding periodic gaits in the presence of discontinuities. Zbl 0987.70007 Adolfsson, Jesper; Dankowicz, Harry; Nordmark, Arne 11 2001 On the origin and bifurcations of stick-slip oscillations. Zbl 0963.70016 Dankowicz, Harry; Nordmark, Arne B. 81 2000 On normal form calculations in impact oscillators. Zbl 0968.34008 Fredriksson, Mats H.; Nordmark, Arne B. 32 2000 Experiments on the onset of impacting motion using a pipe conveying fluid. Zbl 0965.70003 Fredriksson, Mats H.; Borglund, Dan; Nordmark, Arne B. 4 1999 Systems with a preferred spin direction. Zbl 0930.70014 Nordmark, A.; Essén, Hanno 2 1999 Bifurcations caused by grazing incidence in many degrees of freedom impact oscillators. Zbl 0887.70016 Fredriksson, Mats H.; Nordmark, Arne B. 33 1997 Effects due to low velocity impact in mechanical oscillators. Zbl 0900.70304 Nordmark, A. B. 20 1992 all cited Publications top 5 cited Publications all top 5 Cited by 713 Authors 18 Simpson, David John Warwick 15 Piiroinen, Petri T. 15 Tang, Sanyi 14 Nordmark, Arne B. 12 Dankowicz, Harry J. 12 di Bernardo, Mario 12 Du, Zhengdong 12 Xu, Wei 11 Luo, Albert C. J. 10 Kowalczyk, Piotr 9 Zhusubaliev, Zhanybaĭ Tursunbaevich 8 Gardini, Laura 8 Huang, Lihong 8 Qin, Wenjie 8 Xiao, Yanni 7 Champneys, Alan R. 7 Chen, Hebai 7 Jeffrey, Mike R. 7 Mosekilde, Erik 7 Wiercigroch, Marian 7 Xie, Jianhua 6 Akhmet, Marat Ubaydulla 6 Eriksson, Anders B. 6 Gendelman, Oleg V. 6 Li, Shuangbao 6 Li, Yurong 6 Tang, Guangyao 6 Wang, Jiafu 6 Zhang, Wei 5 Banerjee, Soumitro 5 Han, Maoan 5 Hao, Yuxin 5 Legrand, Mathias 5 Li, Denghui 5 Páez Chávez, Joseph Nikolai 5 Pagano, Daniel Juan 5 Pavlovskaia, Ekaterina E. 5 Ponce, Enrique 5 Teixeira, Marco Antonio 5 Wen, Guilin 5 Xiang, Changcheng 5 Yin, Shan 5 Zhang, Weinian 4 Angulo, Fabiola 4 Brogliato, Bernard 4 Dasgupta, Anirvan 4 Fu, Shihui 4 Glendinning, Paul Alexander 4 Hogan, S. John 4 Li, Qunhong 4 Li, Shimin 4 Liu, Yang 4 Makrooni, Roya 4 Nijmeijer, Henk 4 Rachinskii, Dmitrii I. 4 Sushko, Iryna 4 Taborda, John Alexander 4 Tan, Xuewen 4 Tang, Biao 4 Tang, Yilei 4 Várkonyi, Péter László 4 Wagg, David J. 4 Wang, Liang 4 Yang, Xiaosong 4 Yu, Pei 4 Yue, Yuan 3 Avrutin, Viktor 3 Bi, Qinsheng 3 Bondarev, Anton 3 Budd, Christopher John 3 Caldas, Iberê L. 3 Cao, Qingjie 3 Chen, Xingwu 3 Cristiano, Rony 3 de Souza, Silvio Luiz Thomaz 3 Hamdallah, Soliman A. A. 3 Homer, Martin E. 3 Hosham, Hany A. 3 Ivanov, Aleksandr Pavlovich 3 Ji, Jinchen 3 Junca, Stéphane 3 Küpper, Tassilo 3 Leine, Remco I. 3 Li, Liping 3 Li, Wenxiu 3 Liang, Feng 3 Liu, Caishan 3 Liu, Changjian 3 Liu, Xinzhi 3 Lu, Qishao 3 Olivar, Gerard 3 Or, Yizhar 3 Patil, Amit 3 Shi, Xiaotao 3 Staunton, Eoghan J. 3 Wang, Aili 3 Xiong, Yanqin 3 Xu, Huidong 3 Xu, Jieqiong 3 Yang, Guidong ...and 613 more Authors all top 5 Cited in 105 Serials 68 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 50 Nonlinear Dynamics 40 Physica D 31 Chaos, Solitons and Fractals 27 Communications in Nonlinear Science and Numerical Simulation 19 Chaos 13 SIAM Journal on Applied Dynamical Systems 8 Physics Letters. A 8 Mathematics and Computers in Simulation 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 European Journal of Mechanics. A. Solids 8 Nonlinear Analysis. Real World Applications 8 Nonlinear Analysis. Hybrid Systems 7 Applied Mathematics and Computation 7 Journal of Differential Equations 6 European Journal of Physics 6 Regular and Chaotic Dynamics 5 Discrete and Continuous Dynamical Systems. Series B 4 Meccanica 4 Computational Mechanics 4 Mathematical Problems in Engineering 4 Journal of Theoretical Biology 4 AMM. Applied Mathematics and Mechanics. (English Edition) 3 Computers & Mathematics with Applications 3 Computer Methods in Applied Mechanics and Engineering 3 Journal of Mathematical Biology 3 Bulletin of Mathematical Biology 3 Automatica 3 European Journal of Applied Mathematics 3 SIAM Review 3 Multibody System Dynamics 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Qualitative Theory of Dynamical Systems 3 Dynamical Systems 3 Advances in Difference Equations 3 Acta Mechanica Sinica 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Acta Mechanica 2 Journal of Computational Physics 2 Journal of Fluid Mechanics 2 Journal of Mathematical Analysis and Applications 2 Mathematical Biosciences 2 Nonlinearity 2 International Journal for Numerical Methods in Engineering 2 Journal of Computational and Applied Mathematics 2 Journal of Economic Dynamics & Control 2 Applied Mathematical Modelling 2 Automation and Remote Control 2 SIAM Journal on Applied Mathematics 2 Journal of Dynamics and Differential Equations 2 Archive of Applied Mechanics 2 Journal of Nonlinear Science 2 Journal of Computational Neuroscience 2 Complexity 2 Journal of Difference Equations and Applications 2 Journal of Vibration and Control 2 Differential Equations and Dynamical Systems 2 Abstract and Applied Analysis 2 Discrete Dynamics in Nature and Society 2 Mathematical Biosciences and Engineering 2 Journal of Applied Analysis and Computation 1 International Journal of Control 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Applied Mathematics and Mechanics 1 Journal of the Mechanics and Physics of Solids 1 Physica A 1 Physics Reports 1 Wave Motion 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Prikladnaya Matematika i Mekhanika 1 Geometriae Dedicata 1 Theoretical Population Biology 1 Applied Mathematics and Mechanics. (English Edition) 1 Chinese Annals of Mathematics. Series B 1 Mathematical and Computer Modelling 1 Dynamics and Stability of Systems 1 International Journal of Robust and Nonlinear Control 1 New Zealand Journal of Mathematics 1 Journal of Mathematical Sciences (New York) 1 Filomat 1 Bulletin des Sciences Mathématiques 1 Discrete and Continuous Dynamical Systems 1 Optimization Methods & Software 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 European Journal of Mechanics. B. Fluids 1 Acta Mathematica Sinica. English Series 1 Acta Mathematica Scientia. Series A. (Chinese Edition) 1 Iranian Journal of Science and Technology. Transaction A: Science 1 Entropy 1 Journal of Machine Learning Research (JMLR) 1 Communications on Pure and Applied Analysis 1 Foundations of Physics 1 Boundary Value Problems 1 Journal of Biological Dynamics 1 Discrete and Continuous Dynamical Systems. Series S 1 São Paulo Journal of Mathematical Sciences 1 Armenian Journal of Mathematics 1 Advances in Mathematical Physics 1 Science China. Mathematics ...and 5 more Serials all top 5 Cited in 26 Fields 243 Ordinary differential equations (34-XX) 185 Dynamical systems and ergodic theory (37-XX) 140 Mechanics of particles and systems (70-XX) 69 Biology and other natural sciences (92-XX) 54 Mechanics of deformable solids (74-XX) 38 Systems theory; control (93-XX) 22 Numerical analysis (65-XX) 15 Information and communication theory, circuits (94-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Fluid mechanics (76-XX) 8 Partial differential equations (35-XX) 7 Difference and functional equations (39-XX) 6 Probability theory and stochastic processes (60-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Optics, electromagnetic theory (78-XX) 1 Approximations and expansions (41-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) 1 Mathematics education (97-XX) Citations by Year