{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T07:56:04Z","timestamp":1767167764066,"version":"build-2238731810"},"reference-count":2,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2000,5]]},"abstract":"<jats:p>Inverted pendulums are very suitable to illustrate many ideas in automatic control of nonlinear systems. The rotational inverted pendulum is a novel design that has some interesting dynamics features that are not present in inverted pendulums with linear motion of the pivot. In this paper the dynamics of a rotational inverted pendulum has been studied applying well-known results of bifurcation theory. Two classes of local bifurcations are analyzed by means of the center manifold theorem and the normal form theory \u2014 first, a pitchfork bifurcation that appears for the open-loop controlled system; second, a Hopf bifurcation, and its possible degeneracies, of the equilibrium point at the upright pendulum position, that is present for the controlled closed-loop system. Some numerical results are also presented in order to verify the validity of our analysis.<\/jats:p>","DOI":"10.1142\/s0218127400000700","type":"journal-article","created":{"date-parts":[[2003,5,7]],"date-time":"2003-05-07T04:18:55Z","timestamp":1052281135000},"page":"981-995","source":"Crossref","is-referenced-by-count":12,"title":["LOCAL BIFURCATION ANALYSIS IN THE FURUTA PENDULUM VIA NORMAL FORMS"],"prefix":"10.1142","volume":"10","author":[{"given":"DANIEL","family":"PAGANO","sequence":"first","affiliation":[{"name":"Departamento de Automa\u00e7\u00e3o e Sistemas, Universidade Federal de Santa Catarina, 88040-900, Florian\u00f3polis, Brazil"}]},{"given":"LUIS","family":"PIZARRO","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada II, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s\/n, 41092, Sevilla, Spain"}]},{"given":"JAVIER","family":"ARACIL","sequence":"additional","affiliation":[{"name":"Departamento Ingenier\u00eda de Sistemas y  Autom\u00e1tica, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s\/n, 41092, Sevilla, Spain"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"p_3","first-page":"37","author":"\u00c4str\u00f6m K. J.","year":"1996","journal-title":"Proc. 13th IFAC World Congress, San Francisco, USA"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1243\/PIME_PROC_1992_206_043_02"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127400000700","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:03:46Z","timestamp":1565139826000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127400000700"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,5]]},"references-count":2,"aliases":["10.1016\/s0218-1274(00)00070-0"],"journal-issue":{"issue":"05","published-online":{"date-parts":[[2012,5,2]]},"published-print":{"date-parts":[[2000,5]]}},"alternative-id":["10.1142\/S0218127400000700"],"URL":"https:\/\/doi.org\/10.1142\/s0218127400000700","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,5]]}}}