@Article {1,
    author = {J.H. Maddocks},
    title = {Stability of the elastica},
    journal = {Systems of Nonlinear Partial Differential Equations - Proc. of 
        NATO/London Math. Soc. Advanced Study Institute, Eds. J.M. Ball, 
        Reidel},
    year = {1983},
    volume = {},
    number = {},
    month = {},
    pages = {311 - 322},
    abstract = {Systems of Nonlinear Partial Differential Equations - Proc. of 
        NATO/London Math. Soc. Advanced Study Institute (1983) Eds. J.M. Ball, 
        Reidel, 311-322 Sorry, no postscript available Abstract This paper 
        describes previously unknown stabilites and instabilities of planar 
        equilibrium configurations of a nonlinearly elastic rod that is 
        buckled under the action of a dead-load. The governing equations are 
        derived from variational principles, including ones of isoperimetric 
        type. Properties of stability are accordingly determined by study of 
        the second variation. Stabilities to deformations both in the plane 
        and out of the plane are considered. Among the newly discovered 
        properties are: secondary bifurcation from the first buckled mode, 
        marked differences between stability to two-dimensional and to 
        three-dimensional variations, and the stabilizing influence of 
        resistance to twist. In the isoperimetric examples, the analysis makes 
        crucial use of a novel device to account for the dependence of the 
        second variation on constraints.},
    info = {},
    files = {},
    links = {},
    keywords = {}
}

{"_id":"sb9ub8ZdQDSdL7CtE","bibbaseid":"maddocks-stabilityoftheelastica-1983","downloads":0,"creationDate":"2017-08-15T12:38:53.755Z","title":"Stability of the elastica","author_short":["Maddocks, J."],"year":1983,"bibtype":"article","biburl":"http://lcvmwww.epfl.ch/publications/data/articles/1/bibtex.bib","bibdata":{"bibtype":"article","type":"article","author":[{"firstnames":["J.H."],"propositions":[],"lastnames":["Maddocks"],"suffixes":[]}],"title":"Stability of the elastica","journal":"Systems of Nonlinear Partial Differential Equations - Proc. of NATO/London Math. Soc. Advanced Study Institute, Eds. J.M. Ball, Reidel","year":"1983","volume":"","number":"","month":"","pages":"311 - 322","abstract":"Systems of Nonlinear Partial Differential Equations - Proc. of NATO/London Math. Soc. Advanced Study Institute (1983) Eds. J.M. Ball, Reidel, 311-322 Sorry, no postscript available Abstract This paper describes previously unknown stabilites and instabilities of planar equilibrium configurations of a nonlinearly elastic rod that is buckled under the action of a dead-load. The governing equations are derived from variational principles, including ones of isoperimetric type. Properties of stability are accordingly determined by study of the second variation. Stabilities to deformations both in the plane and out of the plane are considered. Among the newly discovered properties are: secondary bifurcation from the first buckled mode, marked differences between stability to two-dimensional and to three-dimensional variations, and the stabilizing influence of resistance to twist. In the isoperimetric examples, the analysis makes crucial use of a novel device to account for the dependence of the second variation on constraints.","info":"","files":"","links":"","keywords":"","bibtex":"@Article {1,\n author = {J.H. Maddocks},\n title = {Stability of the elastica},\n journal = {Systems of Nonlinear Partial Differential Equations - Proc. of \n NATO/London Math. Soc. Advanced Study Institute, Eds. J.M. Ball, \n Reidel},\n year = {1983},\n volume = {},\n number = {},\n month = {},\n pages = {311 - 322},\n abstract = {Systems of Nonlinear Partial Differential Equations - Proc. of \n NATO/London Math. Soc. Advanced Study Institute (1983) Eds. J.M. Ball, \n Reidel, 311-322 Sorry, no postscript available Abstract This paper \n describes previously unknown stabilites and instabilities of planar \n equilibrium configurations of a nonlinearly elastic rod that is \n buckled under the action of a dead-load. The governing equations are \n derived from variational principles, including ones of isoperimetric \n type. Properties of stability are accordingly determined by study of \n the second variation. Stabilities to deformations both in the plane \n and out of the plane are considered. Among the newly discovered \n properties are: secondary bifurcation from the first buckled mode, \n marked differences between stability to two-dimensional and to \n three-dimensional variations, and the stabilizing influence of \n resistance to twist. In the isoperimetric examples, the analysis makes \n crucial use of a novel device to account for the dependence of the \n second variation on constraints.},\n info = {},\n files = {},\n links = {},\n keywords = {}\n}\n","author_short":["Maddocks, J."],"key":"1","id":"1","bibbaseid":"maddocks-stabilityoftheelastica-1983","role":"author","urls":{},"downloads":0},"search_terms":["stability","elastica","maddocks"],"keywords":[],"authorIDs":["5992eb5ddd1dc7cd15000022"],"dataSources":["q2F2detGLvtpWTHGA"]}