{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T09:28:01Z","timestamp":1758274081800},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2009,3,9]],"date-time":"2009-03-09T00:00:00Z","timestamp":1236556800000},"content-version":"unspecified","delay-in-days":4634,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[1996,7]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>The main objective of this work is to study the performance of a flexible single hub-arm system. The equations of motion are derived using the extended Hamilton principle. The Liapunov functional is used as a condition for the stability analysis. The Liapunov functional is considered as the sum of the internal energy of the flexible beam. The required drive torque was obtained directly through the solution of the inverse dynamic problem. Although the flexible link is nonminimum phase in nature, the use of Liapunov and the PD controller guarantee the causality for the stable case. The effects of tip mass as well as its inertia in the case of stable and asymptotic stable systems were investigated to ensure the validity of this procedure.<\/jats:p>","DOI":"10.1017\/s0263574700019779","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T13:09:54Z","timestamp":1236690594000},"page":"381-389","source":"Crossref","is-referenced-by-count":7,"title":["Causal inverse dynamics of a flexible hub-arm system through Liapunov's second method"],"prefix":"10.1017","volume":"14","author":[{"given":"Atef","family":"Ata","sequence":"first","affiliation":[]},{"given":"Salwa","family":"Elkhoga","sequence":"additional","affiliation":[]},{"given":"Mohamed","family":"Shalaby","sequence":"additional","affiliation":[]},{"given":"Shihab","family":"Asfour","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,3,9]]},"reference":[{"key":"S0263574700019779_ref015","volume-title":"Dynamics of Structures","author":"Claugh","year":"1976"},{"key":"S0263574700019779_ref011","unstructured":"Kown D. and Book W.J. . \u201cAn Inverse Dynamic Method Yielding Flexible Maniplator State Trajectory\u201d Proceeding of the 1990 American Control Conference (1990) pp. 186\u2013193."},{"key":"S0263574700019779_ref001","article-title":"Dynamic Analysis of Planar Flexible Mechanisms","volume":"24","author":"Song","year":"1984","journal-title":"Comp. Meth. Appl. Mech. Engn."},{"key":"S0263574700019779_ref008","article-title":"Inverse Dynamics of a Single Link Flexible Robot Analytical and Experimental Results","volume":"3","author":"Bayo.","year":"1988","journal-title":"J. Robotics and Automation"},{"key":"S0263574700019779_ref004","doi-asserted-by":"publisher","DOI":"10.1177\/027836498700600106"},{"key":"S0263574700019779_ref003","doi-asserted-by":"publisher","DOI":"10.1115\/1.3267343"},{"key":"S0263574700019779_ref012","unstructured":"Lam E. \u201cModeling of the UNLV-ARO Light Weight Robot Using Lagrange';s Assumed Mode Method, Sympolic Manipulation and Numerical Simulation\u201d M.S. Thesis (UNLV. 1991)."},{"key":"S0263574700019779_ref006","article-title":"Initial Experiment on End Point Motion of a Single Link Flexible Robot","volume":"6","author":"Cannon","year":"1984","journal-title":"Int. J. Robotics Research."},{"key":"S0263574700019779_ref014","volume-title":"Free Vibration Analysis of Beams and Shafts","author":"Gorman","year":"1975"},{"key":"S0263574700019779_ref013","volume-title":"Analytical Methods in Vibration","author":"Meirovitch","year":"1967"},{"key":"S0263574700019779_ref002","doi-asserted-by":"publisher","DOI":"10.1177\/027836498400300305"},{"key":"S0263574700019779_ref005","article-title":"On the Dynamics of Flexible Beams Under Large Overall Motion, the Plan Case","volume":"41","author":"Simo","year":"1986","journal-title":"ASME Paper"},{"key":"S0263574700019779_ref009","doi-asserted-by":"publisher","DOI":"10.1177\/027836498900800604"},{"key":"S0263574700019779_ref007","article-title":"A Finite Element Approach to Control the End Point Motion of a Single Link Flexible Robot","volume":"4","author":"Bayo","year":"1987","journal-title":"Int. J. Robotics Systems"},{"key":"S0263574700019779_ref010","doi-asserted-by":"publisher","DOI":"10.2514\/3.20740"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574700019779","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T21:09:30Z","timestamp":1557695370000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574700019779\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,7]]},"references-count":15,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1996,7]]}},"alternative-id":["S0263574700019779"],"URL":"https:\/\/doi.org\/10.1017\/s0263574700019779","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,7]]}}}