Asymptotic solutions to the non-linear cantilever elastica

Stampouloglou, I. H.; Theotokoglou, Efstathios E.; Andriotaki, P.N.

doi:10.1016/j.ijnonlinmec.2005.05.003

Cited by 5 publications

(2 citation statements)

References 3 publications

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“…In particular, the following questions arose, which are important for applications to engineering: what is the behaviour of a compressed rack under loads higher than the Euler critical value, what is the shape of the rack in this case, is it unique and stable? A number of papers (see [49], [69], [75], [96], [119], [148], [149], [161]) were concerned with these questions, considering various conditions for supporting and loading inextensible elastic rods. During the last decades the interest to elasticae has grown because of applications of the theory of flexible rods to the analysis of micro-and nanostructures in biology and nanotechnology [76], [84], [115], [151].…”

Section: Existence and Boundedness Of Optimal Controlsmentioning

confidence: 99%

Left-invariant optimal control problems on Lie groups that are integrable by elliptic functions

Sachkov

2023

Russian Math. Surveys

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Left-invariant optimal control problems on Lie groups are an important class of problems with a large symmetry group. They are theoretically interesting because they can often be investigated in full and general laws can be studied by using these model problems. In particular, problems on nilpotent Lie groups provide a fundamental nilpotent approximation to general problems. Also, left-invariant problems often arise in applications such as classical and quantum mechanics, geometry, robotics, visual perception models, and image processing. The aim of this paper is to present a survey of the main concepts, methods, and results pertaining to left-invariant optimal control problems on Lie groups that can be integrated by elliptic functions. The focus is on describing extremal trajectories and their optimality, the cut time and cut locus, and optimal synthesis. Bibliography: 162 titles.

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Section: Existence and Boundedness Of Optimal Controlsmentioning

confidence: 99%

Left-invariant optimal control problems on Lie groups that are integrable by elliptic functions

Sachkov

2023

Russian Math. Surveys

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show abstract

“…Is this configuration unique and is it stable? These issues have been a subject of numerous publications [3,8,20,14,28,42,35,39,34,40] (see also the references therein) in which equilibrium states of inextensible unshearable rods subject to various loading and boundary conditions have been studied. In the last decades, elasticae have attracted increasing interest in connection with application of the rod theories to the analysis of micro-and nanostructures in biology and nanotechnology [21,41,33,23].…”

Section: Introductionmentioning

confidence: 99%