Shil'nikov homoclinic dynamics and the escape from roll autorotation in an F–4 model

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Lowenberg M. H. and Champneys A. R. 1998Shil'nikov homoclinic dynamics and the escape from roll autorotation in an F–4 modelPhil. Trans. R. Soc. A.3562241–2256http://doi.org/10.1098/rsta.1998.0272SectionRestricted accessShil'nikov homoclinic dynamics and the escape from roll autorotation in an F–4 model M. H. Lowenberg M. H. Lowenberg Department of Aerospace Engineering, University of Bristol, Queen's Building, University Walk, Bristol BS8 1TR, UK Google Scholar Find this author on PubMed Search for more papers by this author and A. R. Champneys A. R. Champneys Department of Engineering Mathematics, University of Bristol, Queen's Building, University Walk, Bristol BS8 1TR, UK Google Scholar Find this author on PubMed Search for more papers by this author M. H. Lowenberg M. H. Lowenberg Department of Aerospace Engineering, University of Bristol, Queen's Building, University Walk, Bristol BS8 1TR, UK Google Scholar Find this author on PubMed Search for more papers by this author and A. R. Champneys A. R. Champneys Department of Engineering Mathematics, University of Bristol, Queen's Building, University Walk, Bristol BS8 1TR, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:15 October 1998https://doi.org/10.1098/rsta.1998.0272AbstractAn investigation is undertaken into the nonlinear dynamics of an 8th–order model for the F–4J Phantom fighter aircraft in a neighbourhood of its autorotation flight regime. This regime is characterized by high roll rates with no roll control inputs. It is found that the basic state goes unstable via a supercritical Hopf bifurcation as the value of the stabilator (the pitch axis control surface) is increased (i.e. the control column is pushed forward). The ensuing stable limit cycle behaviour is itself destroyed at a higher stabilator value in a certain homoclinic bifurcation first analysed by Shil'nikov. A careful numerical continuation analysis is performed using spline interpolation of the tabulated data in the model. The limit cycle is found to reach infinite period along a complex wiggly bifurcation curve, as predicted by the theory of Shil'nikov homoclinic orbits. Several period–doubling and secondary–Hopf (torus) bifurcations are discovered. Direct simulation of the aircraft dynamics, using linear interpolation of the data, is shown to give good agreement with the continuation results. It is found that the homoclinic bifurcation marks an escape from autorotation. That is, varying stabilator slowly through the critical value results in a jump from oscillatory autorotation to symmetric flight. Possible implications of these results for other flight phenomena are discussed. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Paranjape A and Ananthkrishnan N (2012) The Bifurcation and Continuation Method from an Aerospace Systems Design Point of View AIAA Atmospheric Flight Mechanics Conference, 10.2514/6.2012-4408, 978-1-62410-184-7, Online publication date: 13-Aug-2012. Pauck S and Engelbrecht J (2012) Bifurcation Analysis of the Generic Transport Model with a view to Upset Recovery AIAA Atmospheric Flight Mechanics Conference, 10.2514/6.2012-4646, 978-1-62410-184-7, Online publication date: 13-Aug-2012. Żbikowski R, Ansari S and Knowles K (2006) On mathematical modelling of insect flight dynamics in the context of micro air vehicles, Bioinspiration & Biomimetics, 10.1088/1748-3182/1/2/R02, 1:2, (R26-R37), Online publication date: 1-Jun-2006. Richardson T, Charles G, Stoten D, di Bernardo M and Lowenberg M Continuation based control of aircraft dynamics 42nd IEEE International Conference on Decision and Control, 10.1109/CDC.2003.1272402, 0-7803-7924-1, (4932-4938) Lowenberg M (1998) Development of control schedules to modify spin behaviour 23rd Atmospheric Flight Mechanics Conference, 10.2514/6.1998-4267, , Online publication date: 10-Aug-1998. This Issue15 October 1998Volume 356Issue 1745Theme Issue ‘Nonlinear flight dynamics of high-performance aircraft’ compiled by J. M. T. Thompson and F. B. J. Macmillen Article InformationDOI:https://doi.org/10.1098/rsta.1998.0272Published by:Royal SocietyPrint ISSN:1364-503XOnline ISSN:1471-2962History: Published online15/10/1998Published in print15/10/1998 License: Citations and impact Keywordsnumerical continuationflight dynamicsglobal bifurcationnonlinear dynamicsautorotation