General information
Latest issue
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Avtomat. i Telemekh.:

Personal entry:
Save password
Forgotten password?

Avtomat. i Telemekh., 2009, Issue 4, Pages 78–88 (Mi at452)  

This article is cited in 10 scientific papers (total in 10 papers)

Systems with Lumped Parameters

Solution to Euler's elastic problem

A. A. Ardentov, Yu. L. Sachkov

Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalesskii, Russia

Abstract: Euler's problem on stationary configurations of elastic rod with fixed endpoints and tangents at the endpoints is considered. The corresponding optimal control problem is reduced to several systems of algebraic equations in Jacobi's functions. An algorithm and software for solving the optimal control problem are constructed.

Full text: PDF file (751 kB)
References: PDF file   HTML file

English version:
Automation and Remote Control, 2009, 70:4, 633–643

Bibliographic databases:

PACS: 02.30.Yy
Presented by the member of Editorial Board: . . 

Received: 01.10.2008

Citation: A. A. Ardentov, Yu. L. Sachkov, “Solution to Euler's elastic problem”, Avtomat. i Telemekh., 2009, no. 4, 78–88; Autom. Remote Control, 70:4 (2009), 633–643

Citation in format AMSBIB
\by A.~A.~Ardentov, Yu.~L.~Sachkov
\paper Solution to Euler's elastic problem
\jour Avtomat. i Telemekh.
\yr 2009
\issue 4
\pages 78--88
\jour Autom. Remote Control
\yr 2009
\vol 70
\issue 4
\pages 633--643

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Ardentov, Yu. L. Sachkov, “Extremal trajectories in a nilpotent sub-Riemannian problem on the Engel group”, Sb. Math., 202:11 (2011), 1593–1615  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Hahn J., Chung G.J., Wang Yu., Tai X.-Ch., “Fast Algorithms for P-Elastica Energy with the Application to Image Inpainting and Curve Reconstruction”, Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, 6667, eds. Bruckstein A., Romeny B., Bronstein A., Bronstein M., Springer-Verlag Berlin, 2012, 169–182  crossref  isi  scopus
    3. Carroll D., Hankins E., Kose E., Sterling I., “a Survey of the Differential Geometry of Discrete Curves”, Math. Intell., 36:4 (2014), 28–35  crossref  mathscinet  zmath  isi  scopus
    4. Sachkov Yu.L., Sachkova E.F., “Exponential Mapping in Euler'S Elastic Problem”, J. Dyn. Control Syst., 20:4 (2014), 443–464  crossref  mathscinet  zmath  isi  scopus
    5. Duits R., Boscain U., Rossi F., Sachkov Y., “Association Fields Via Cuspless Sub-Riemannian Geodesics in Se(2)”, J. Math. Imaging Vis., 49:2 (2014), 384–417  crossref  mathscinet  zmath  isi  elib  scopus
    6. Ivan A. Bizyaev, Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Integrability and Nonintegrability of Sub-Riemannian Geodesic Flows on Carnot Groups”, Regul. Chaotic Dyn., 21:6 (2016), 759–774  mathnet  crossref  mathscinet
    7. Andrey A. Ardentov, “Controlling of a Mobile Robot with a Trailer and Its Nilpotent Approximation”, Regul. Chaotic Dyn., 21:7-8 (2016), 775–791  mathnet  crossref
    8. Alexey Mashtakov, Andrei Ardentov, Yuri L. Sachkov, “Relation Between Eulers Elasticae and Sub-Riemannian Geodesics on $SE(2)$”, Regul. Chaotic Dyn., 21:7-8 (2016), 832–839  mathnet  crossref
    9. A. A. Ardentov, “Multiple solutions in Euler's elastic problem”, Autom. Remote Control, 79:7 (2018), 1191–1206  mathnet  crossref  isi  elib
    10. Ardentov A.A. Karavaev Yu.L. Yefremov K.S., “Euler Elasticas For Optimal Control of the Motion of Mobile Wheeled Robots: the Problem of Experimental Realization”, Regul. Chaotic Dyn., 24:3 (2019), 312–328  crossref  isi
  • Avtomatika i Telemekhanika
    Number of views:
    This page:376
    Full text:127
    First page:4

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019