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Mat. Sb., 2006, Volume 197, Number 2, Pages 95–116 (Mi msb1514)  

This article is cited in 18 scientific papers (total in 18 papers)

Discrete symmetries in the generalized Dido problem

Yu. L. Sachkov

Program Systems Institute of RAS

Abstract: The generalized Dido problem is considered — a model of the nilpotent sub-Riemannian problem with the growth vector $(2, 3, 5)$. The group of discrete symmetries in this problem is constructed as an extension of the reflection group of the standard mathematical pendulum. The action of these symmetries in the inverse image and image of the exponential map is studied.
Bibliography: 16 titles.

DOI: https://doi.org/10.4213/sm1514

Full text: PDF file (656 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2006, 197:2, 235–257

Bibliographic databases:

UDC: 517.977
MSC: Primary 53C17; Secondary 17B66, 49J15, 53C22, 93C15
Received: 28.03.2005

Citation: Yu. L. Sachkov, “Discrete symmetries in the generalized Dido problem”, Mat. Sb., 197:2 (2006), 95–116; Sb. Math., 197:2 (2006), 235–257

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. L. Sachkov, “Complete description of the Maxwell strata in the generalized Dido problem”, Sb. Math., 197:6 (2006), 901–950  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Yu. L. Sachkov, “The Maxwell set in the generalized Dido problem”, Sb. Math., 197:4 (2006), 595–621  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Yu. L. Sachkov, “Optimality of Euler's elasticae”, Dokl. Math., 76:3 (2007), 817–819  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. Sachkov Yu.L., “Maxwell strata in the Euler elastic problem”, J. Dyn. Control Syst., 14:2 (2008), 169–234  crossref  mathscinet  zmath  isi  elib  scopus
    5. Yu. L. Sachkov, “Control theory on Lie groups”, Journal of Mathematical Sciences, 156:3 (2009), 381–439  mathnet  crossref  mathscinet  zmath  elib
    6. A. A. Ardentov, Yu. L. Sachkov, “Solution to Euler's elastic problem”, Autom. Remote Control, 70:4 (2009), 633–643  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    7. Gurman V.I., Sachkov Yu.L., “Issledovatelskii tsentr protsessov upravleniya: 1988–2008 gg.”, Istoriya nauki i tekhniki, 2009, no. 5, 81–88  mathscinet  elib
    8. Gurman A.I., Sachkov Yu.L., “Issledovatelskii tsentr protsessov upravleniya: 1988–2008 gg.”, Promyshlennye ASU i kontrollery, 2009, no. 9, 25–30  elib
    9. Yu. L. Sachkov, “Maxwell strata and symmetries in the problem of optimal rolling of a sphere over a plane”, Sb. Math., 201:7 (2010), 1029–1051  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Sachkov Yu.L., “Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane”, ESAIM Control Optim. Calc. Var., 16:4 (2010), 1018–1039  crossref  mathscinet  zmath  isi  elib  scopus
    11. Moiseev I., Sachkov Yu.L., “Maxwell strata in sub-Riemannian problem on the group of motions of a plane”, ESAIM Control Optim. Calc. Var., 16:2 (2010), 380–399  crossref  mathscinet  zmath  isi  elib  scopus
    12. A. P. Mashtakov, “Algoritmicheskoe i programmnoe obespechenie resheniya konstruktivnoi zadachi upravleniya negolonomnymi pyatimernymi sistemami”, Programmnye sistemy: teoriya i prilozheniya, 3:1 (2012), 3–29  mathnet
    13. Ya.A.wais Butt, Yu.L.. Sachkov, A.I.qbal Bhatti, “Extremal Trajectories and Maxwell Strata in Sub-Riemannian Problem on Group of Motions of Pseudo-Euclidean Plane”, J Dyn Control Syst, 2014  crossref  mathscinet  scopus
    14. Boscain U., Duits R., Rossi F., Sachkov Yu., “Curve Cuspless Reconstruction Via Sub-Riemannian Geometry”, ESAIM-Control OPtim. Calc. Var., 20:3 (2014), 748–770  crossref  mathscinet  zmath  isi  elib  scopus
    15. J.-P. Gauthier, Yu. L. Sachkov, “On the free Carnot (2,3,5,8) group”, Programmnye sistemy: teoriya i prilozheniya, 6:2 (2015), 45–61  mathnet
    16. Butt Ya.A., Sachkov Yu.L., Bhatti A.I., “Maxwell Strata and Conjugate Points in the Sub-Riemannian Problem on the Lie Group SH(2)”, J. Dyn. Control Syst., 22:4 (2016), 747–770  crossref  mathscinet  zmath  isi  scopus
    17. Sachkov Yu.L. Sachkova E.F., “Degenerate abnormal trajectories in a sub-Riemannian problem with growth vector (2, 3, 5, 8)”, Differ. Equ., 53:3 (2017), 352–365  mathnet  crossref  mathscinet  zmath  isi  scopus
    18. L. V. Lokutsievskiy, Yu. L. Sachkov, “Liouville integrability of sub-Riemannian problems on Carnot groups of step 4 or greater”, Sb. Math., 209:5 (2018), 672–713  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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