{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,11]],"date-time":"2025-01-11T22:10:23Z","timestamp":1736633423662,"version":"3.32.0"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2006,11,7]],"date-time":"2006-11-07T00:00:00Z","timestamp":1162857600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nonlinear Dyn"],"published-print":{"date-parts":[[2007,1,18]]},"DOI":"10.1007\/s11071-006-9035-y","type":"journal-article","created":{"date-parts":[[2006,11,6]],"date-time":"2006-11-06T15:25:52Z","timestamp":1162826752000},"page":"363-366","source":"Crossref","is-referenced-by-count":10,"title":["The dynamical nature of a backlash system with and without fluid friction"],"prefix":"10.1007","volume":"47","author":[{"given":"R. Vilela","family":"Mendes","sequence":"first","affiliation":[]},{"given":"Luis","family":"V\u00e1zquez","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2006,11,7]]},"reference":[{"key":"9035_CR1","unstructured":"Special issue on Non-Smooth Mechanics, Phil. Trans. of the Royal Soc. of London: Math., Phys. and Eng. Sciences, 359, (December 15) (2001)"},{"key":"9035_CR2","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1109\/9.341803","volume":"40","author":"G. Tao","year":"1995","unstructured":"Tao, G., Kokotovic, P.V.: Adaptive control of systems with unknown output backlash. IEEE Trans. Autom. Control 40, 326\u2013330 (1995)","journal-title":"IEEE Trans. Autom. Control"},{"key":"9035_CR3","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1115\/1.3143750","volume":"108","author":"Y. Stepanenko","year":"1986","unstructured":"Stepanenko, Y., Sankar, T.S.: Vibro-impact analysis of control systems with mechanical clearance and its application to robotic actuators. ASME J. Dyn. Syst. Meas. Contr. 108, 9\u201316 (1986)","journal-title":"ASME J. Dyn. Syst. Meas. Contr."},{"key":"9035_CR4","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/BF00045670","volume":"2","author":"K. Karagiannis","year":"1991","unstructured":"Karagiannis, K., Pfeiffer, F.: Theoretical and experimental investigations of gear-rattling. Nonlinear Dyn. 2, 367\u2013387 (1991)","journal-title":"Nonlinear Dyn."},{"key":"9035_CR5","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1006\/jsvi.1998.1646","volume":"215","author":"Q. Feng","year":"1998","unstructured":"Feng, Q., Pfeiffer, F.: Stochastic model on a rattling system. J. Sound Vib. 215, 439\u2013453 (1998)","journal-title":"J. Sound Vib."},{"key":"9035_CR6","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/S0022-460X(88)80365-1","volume":"121","author":"H.N. \u00d6zg\u00fcven","year":"1998","unstructured":"\u00d6zg\u00fcven, H.N., Housen, D.R.: Mathematical models used in gear dynamics-a review. J. Sound Vib. 121, 383\u2013411 (1998)","journal-title":"J. Sound Vib."},{"key":"9035_CR7","unstructured":"Faria, M., Streit, L., Vilela Mendes, R.: Map dynamics in gearbox models. In: Proceedings of 2nd European Symposium on Mathematics in Industry, H. Neunzert (ed.) B. G. Teubner, Stuttgart (1988)"},{"key":"9035_CR8","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1016\/0167-2789(88)90038-3","volume":"29","author":"M.O. Hongler","year":"1988","unstructured":"Hongler, M.O., Streit, L.: On the origin of chaos in gearbox models. Phy. D 29, 402\u2013408 (1988)","journal-title":"Phy. D"},{"key":"9035_CR9","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/S0960-0779(02)00452-6","volume":"16","author":"G. Litak","year":"2003","unstructured":"Litak, G., Friswell, M.I.: Vibrations in gear systems. Chaos Solitons Fractals 16, 145\u2013150 (2003)","journal-title":"Chaos Solitons Fractals"},{"key":"9035_CR10","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1023\/A:1016514000260","volume":"29","author":"R.S. Barbosa","year":"2002","unstructured":"Barbosa, R.S., Machado, J.A.T.: Describing function analysis of systems with impacts and backlash. Nonlinear Dyn. 29, 235\u2013250 (2002)","journal-title":"Nonlinear Dyn."},{"key":"9035_CR11","unstructured":"Ma, C., Hori, Y.: Backlash vibration suppression in torsional system based on the fractional order Q-filter of disturbance observer. In: Proceedings of 8th IEEE International Workshop on Advanced Motion Control, Kawasaki, Japan, pp. 577\u2013582 (2004)"},{"key":"9035_CR12","doi-asserted-by":"crossref","unstructured":"Machado, J.A.T., Azenha, A.: Fractional-order hybrid control of robot manipulators. In: Proceedings of IEEE International Conference on Systems, Man and Cybernetics, Hammamet, Tunisia, Vol. 1, pp. 788\u2013793 (1998)","DOI":"10.1109\/ICSMC.1998.725510"},{"key":"9035_CR13","doi-asserted-by":"crossref","unstructured":"Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)","DOI":"10.1142\/9789812817747"},{"key":"9035_CR14","first-page":"449","volume":"3","author":"R. Hilfer","year":"1995","unstructured":"Hilfer, R.; Foundations of fractional dynamics. Fractals 3, 449\u2013556 (1995)","journal-title":"Fractals"},{"key":"9035_CR15","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1115\/1.1478062","volume":"124","author":"V.V. Kulish","year":"2002","unstructured":"Kulish, V.V., Lage, J.L.: Applications of fractional calculus to fluid mechanics. J. Fluids Eng. 124, 803\u2013806 (2002)","journal-title":"J. Fluids Eng."},{"key":"9035_CR16","unstructured":"Jacek, L.: The calculation of a normal force between multiparticle contacts using fractional operators. In: 2nd MIT Conference on Computational Fluid an Solid Mechanics, MA, arXiv: physics\/0209085 (2003)"},{"key":"9035_CR17","unstructured":"Tenreiro Machado, J.A. (ed.): Special issue on fractional order calculus and its applications. Nonlinear Dyn. 29 (2002)"},{"key":"9035_CR18","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1115\/1.3167615","volume":"51","author":"P.J. Torvik","year":"1984","unstructured":"Torvik, P.J., Bagley, R.L.: On the appearance of the fractional derivative in the behavior of real materials. Trans. ASME 51, 294\u2013298 (1984)","journal-title":"Trans. ASME"},{"key":"9035_CR19","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1122\/1.549724","volume":"27","author":"R.L. Bagley","year":"1983","unstructured":"Bagley, R.L.: A theoretical basis for the application of fractional calculus to viscoelasticity. J. Rheol. 27, 201\u2013210 (1983)","journal-title":"J. Rheol."},{"key":"9035_CR20","doi-asserted-by":"crossref","unstructured":"Chatterjee, A.: Statistical origins of fractional derivatives in viscoelasticity. J. Sound Vib., in press (2005)","DOI":"10.1016\/j.jsv.2004.09.019"},{"key":"9035_CR21","doi-asserted-by":"crossref","unstructured":"West, B.J.: Fractional calculus and memory in biophysical time series, in Fractals in Biology and Medicine. Vol. III, pp. 221\u2013234, Birkh\u00e4user, Basel (2003)","DOI":"10.1007\/978-3-0348-8119-7_23"},{"key":"9035_CR22","doi-asserted-by":"crossref","unstructured":"Leszczynski, J.S.: Using the fractional interaction law to model the impact dynamics of multiparticle collisions in arbitrary form. Phys. Rev. E70, 051315 (2004)","DOI":"10.1103\/PhysRevE.70.051315"},{"key":"9035_CR23","unstructured":"Podlubny, I.: Geometric and physical interpretation of fractional integration and fractional differentiation. arXiv:math.CA\/0110241 (2001)"},{"key":"9035_CR24","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1080\/00029890.1988.11972030","volume":"95","author":"G.L. Bullock","year":"1988","unstructured":"Bullock, G.L.: A geometric interpretation of the Riemann-Stieltjes integral. Am. Math. Monthly 95, 448\u2013455 (1988)","journal-title":"Am. Math. Monthly"}],"container-title":["Nonlinear Dynamics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-006-9035-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11071-006-9035-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-006-9035-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,11]],"date-time":"2025-01-11T21:46:06Z","timestamp":1736631966000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11071-006-9035-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,11,7]]},"references-count":24,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,1,18]]}},"alternative-id":["9035"],"URL":"https:\/\/doi.org\/10.1007\/s11071-006-9035-y","relation":{},"ISSN":["0924-090X","1573-269X"],"issn-type":[{"type":"print","value":"0924-090X"},{"type":"electronic","value":"1573-269X"}],"subject":[],"published":{"date-parts":[[2006,11,7]]}}}