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Mat. Sb., 2006, Volume 197, Number 4, Pages 123–150 (Mi msb1548)  

This article is cited in 21 scientific papers (total in 21 papers)

The Maxwell set 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 $(2,3,5)$. We study the Maxwell set, that is, the locus of the intersection points of geodesics of equal lengths. A general description is obtained for the Maxwell strata corresponding to the symmetry group of the exponential map generated by rotations and reflections. The invariant and graphic meaning of these strata is clarified.
Bibliography: 19 titles.


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English version:
Sbornik: Mathematics, 2006, 197:4, 595–621

Bibliographic databases:

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

Citation: Yu. L. Sachkov, “The Maxwell set in the generalized Dido problem”, Mat. Sb., 197:4 (2006), 123–150; Sb. Math., 197:4 (2006), 595–621

Citation in format AMSBIB
\by Yu.~L.~Sachkov
\paper The Maxwell set in the generalized Dido problem
\jour Mat. Sb.
\yr 2006
\vol 197
\issue 4
\pages 123--150
\jour Sb. Math.
\yr 2006
\vol 197
\issue 4
\pages 595--621

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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, “Discrete symmetries in the generalized Dido problem”, Sb. Math., 197:2 (2006), 235–257  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
    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
    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 A.I., Sachkov Yu.L., “Issledovatelskii tsentr protsessov upravleniya: 1988–2008 gg.”, Promyshlennye ASU i kontrollery, 2009, no. 9, 25–30  elib
    8. 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
    9. 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
    10. 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
    11. 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
    12. 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
    13. 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
    14. Butt Ya.A., Bhatti A.I., Sachkov Yu.L., “Integrability By Quadratures in Optimal Control of a Unicycle on Hyperbolic Plane”, 2015 American Control Conference (Acc), Proceedings of the American Control Conference, IEEE, 2015, 4251–4256  crossref  mathscinet  isi
    15. 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
    16. Podobryaev A.V. Sachkov Yu.L., “Symmetric Riemannian Problem on the Group of Proper Isometries of Hyperbolic Plane”, J. Dyn. Control Syst., 24:3 (2018), 391–423  crossref  mathscinet  zmath  isi
    17. A. V. Podobryaev, “Diameter of the Berger Sphere”, Math. Notes, 103:5 (2018), 846–851  mathnet  crossref  crossref  isi  elib
    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  mathscinet  adsnasa  isi  elib
    19. A. V. Podobryaev, “Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems”, Nelineinaya dinam., 15:4 (2019), 569–575  mathnet  crossref  elib
    20. A. V. Podobryaev, “Symmetries in left-invariant optimal control problems”, Sb. Math., 211:2 (2020), 275–290  mathnet  crossref  crossref  isi  elib
    21. Yu. L. Sachkov, “Conjugate Points in the Generalized Dido Problem”, Math. Notes, 108:5 (2020), 761–763  mathnet  crossref  crossref
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