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Then the approximated models are applied to the celtic stone dynamics, however with the significant simplifying assumption of circular contact between stone and the table, presenting differences between them again. Certain specific approximations and regularizations of the friction and rolling resistance models enabling and facilitating their application to the real problem are shown. The analysis of the response dependence on initial conditions is performed by the use of a special kind of diagram.<\/jats:p>","DOI":"10.1142\/s0218127411030222","type":"journal-article","created":{"date-parts":[[2011,9,12]],"date-time":"2011-09-12T08:42:56Z","timestamp":1315816976000},"page":"2905-2917","source":"Crossref","is-referenced-by-count":17,"title":["TANGENS HYPERBOLICUS APPROXIMATIONS OF THE SPATIAL MODEL OF FRICTION COUPLED WITH ROLLING RESISTANCE"],"prefix":"10.1142","volume":"21","author":[{"given":"GRZEGORZ","family":"KUDRA","sequence":"first","affiliation":[{"name":"Department of Automation and Biomechanics (K\u201316), Technical University of Lodz, 1\/15 Stefanowskiego St., 90-924 \u0141\u00f3d\u017a, Poland"}]},{"given":"JAN","family":"AWREJCEWICZ","sequence":"additional","affiliation":[{"name":"Department of Automation and Biomechanics (K\u201316), Technical University of Lodz, 1\/15 Stefanowskiego St., 90-924 \u0141\u00f3d\u017a, Poland"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/9789812564801"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127404011818"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405013290"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2004.12.038"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408022159"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1986.0052"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1070\/PU2003v046n04ABEH001306"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1134\/S1028335806050107"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-0557-2_6"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7462(80)90014-1"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7793-9"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.2001.3809"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1988.0078"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(98)00381-8"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-44479-4"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1088\/0370-1328\/71\/6\/312"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1961.0004"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(96)00025-2"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139171731"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7462(82)90017-8"},{"key":"rf24","first-page":"116","volume":"43","author":"Kireenkov A. 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