{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T06:14:07Z","timestamp":1791267247948,"version":"4.1.0"},"reference-count":74,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>The locomotion of microorganisms and tiny artificial swimmers is governed by low-Reynolds-number hydrodynamics, where viscous effects dominate and inertial effects are negligible. While the theory of low-Reynolds-number locomotion is well studied for unbounded fluid domains, the presence of a boundary has a significant influence on the swimmer's trajectories and poses problems of dynamic stability of its motion. In this paper we consider a simple theoretical model of a microswimmer near a wall, study its dynamics, and analyze the stability of its motion. We highlight the underlying geometric structure of the dynamics, and establish a relation between the reversing symmetry of the system and existence and stability of periodic and steady solutions of motion near the wall. The results are demonstrated by numerical simulations and validated by motion experiments with macroscale robotic swimmer prototypes.<\/jats:p>","DOI":"10.1137\/100808745","type":"journal-article","created":{"date-parts":[[2011,9,20]],"date-time":"2011-09-20T18:21:58Z","timestamp":1316542918000},"page":"1013-1041","source":"Crossref","is-referenced-by-count":23,"title":["Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall"],"prefix":"10.1137","volume":"10","author":[{"given":"Yizhar","family":"Or","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sebastian","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard M.","family":"Murray","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,9,20]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/7\/1\/234"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/10\/6\/063016"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112003005184"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1115\/1.2171439"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.101.038102"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700047134"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1017\/S002211207100048X"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/BF02353701"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112062000026"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"F. 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Cort\u00e9s,\n                      Geometric, Control, and Numerical Aspects of Nonholonomic Systems\n                      , Springer-Verlag, Berlin, Heidelberg, 2002."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1002\/cm.10085"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijnonlinmec.2010.12.010"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2011.223"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.81.036313"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112010004465"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1976-0402815-3"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.102.168101"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1038\/nature04090"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1017\/S002211208700171X"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1007\/BF02461846"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1006\/jcis.2000.6981"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.92.13.6195"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1021\/nl900186w"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1137\/0151005"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1529\/biophysj.105.067553"},{"key":"R29","doi-asserted-by":"crossref","unstructured":"J. Guckenheimer and P. Holmes,\n                      Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields\n                      , Springer-Verlag, New York, 1983.","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"R30","unstructured":"J. Happel and H. Brenner,\n                      Low Reynolds Number Hydrodynamics\n                      , Prentice\u2013Hall, Englewood Cliffs, NJ, 1965."},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1960-0121542-7"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112006002631"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1922.0078"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.74.035302"},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-004-0650-9"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112074001984"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112075003126"},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.103.138103"},{"key":"R39","doi-asserted-by":"publisher","DOI":"10.1002\/rob.4620120607"},{"key":"R40","unstructured":"S. Kim and S. J. Karrila,\n                      Microhydrodynamics\n                      , Butterworth-Heinemann, Boston, 1991."},{"key":"R41","doi-asserted-by":"publisher","DOI":"10.1007\/BF02434055"},{"key":"R42","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2006.889485"},{"key":"R43","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/25\/4\/028"},{"key":"R44","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(97)00199-1"},{"key":"R45","doi-asserted-by":"publisher","DOI":"10.1529\/biophysj.105.069401"},{"key":"R46","doi-asserted-by":"publisher","DOI":"10.1088\/0034-4885\/72\/9\/096601"},{"key":"R47","doi-asserted-by":"publisher","DOI":"10.1063\/1.2939069"},{"key":"R48","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/9\/5\/145"},{"key":"R49","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160050201"},{"key":"R50","doi-asserted-by":"crossref","unstructured":"J. E. Marsden,\n                      Lectures on Mechanics\n                      , Cambridge University Press, New York, 1992.","DOI":"10.1017\/CBO9780511624001"},{"key":"R51","doi-asserted-by":"publisher","DOI":"10.1007\/s11340-010-9349-z"},{"key":"R52","doi-asserted-by":"publisher","DOI":"10.1137\/060649884"},{"key":"R53","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.69.062901"},{"key":"R54","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.82.065302"},{"key":"R55","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.79.045302"},{"key":"R56","doi-asserted-by":"publisher","DOI":"10.1177\/027836499801700701"},{"key":"R57","doi-asserted-by":"publisher","DOI":"10.1063\/1.2930667"},{"key":"R58","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.fl.24.010192.001525"},{"key":"R59","doi-asserted-by":"crossref","unstructured":"C. Pozrikidis,\n                      Boundary Integral and Singularity Methods for Linearized Viscous Flow\n                      , Cambridge University Press, Cambridge, UK, 1992.","DOI":"10.1017\/CBO9780511624124"},{"key":"R60","doi-asserted-by":"publisher","DOI":"10.1119\/1.10903"},{"key":"R61","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(93)81129-9"},{"key":"R62","unstructured":"O. Samson,\n                      Low Reynolds Number Swimming in Complex Environments\n                      , Ph.D. thesis, Department of Mathematics, Imperial College, London, UK, 2010; available online at http:\/\/www2.imperial.ac.uk\/ dgcrowdy\/students\/SamsonThesis.pdf http:\/\/www2.imperial.ac.uk\/ dgcrowdy\/students\/SamsonThesis.pdf."},{"key":"R63","doi-asserted-by":"crossref","unstructured":"M. B. 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Murray,\n                      Experimental demonstration of the dynamics and stability of a low Reynolds number swimmer near a plane wall\n                      , in Proceedings of the American Control Conference, Baltimore, MD, IEEE Press, Piscataway, NJ, 2010, pp. 4205\u20134210.","DOI":"10.1109\/ACC.2010.5530846"},{"key":"R74","doi-asserted-by":"publisher","DOI":"10.1007\/s00227-007-0891-x"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100808745","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:09:05Z","timestamp":1787227745000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100808745"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":74,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1137\/100808745"],"URL":"https:\/\/doi.org\/10.1137\/100808745","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1]]}}}