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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika

TMF, 2002, Volume 131, Number 1, Pages 118–125 (Mi tmf318)

Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops
V. V. Sokolov, A. V. Tsiganov

This publication is cited in the following articles:
  1. V. V. Sokolov, “Integrable Hamiltonians related to the $\mathfrak{e}(3)$, $\mathfrak{so}(4)$, and $\mathfrak{so}(3,1)$ Poisson brackets”, Theoret. and Math. Phys., 223:2 (2025), 742–754  mathnet  crossref  crossref  mathscinet  adsnasa
  2. Velimir Jurdjevic, “Sonya Kowalewski's Legacy to Mechanics and Complex Lie Algebras”, Regul. Chaotic Dyn., 30:5 (2025), 767–798  mathnet  crossref
  3. Bozidar Jovanović, “Contact Magnetic Geodesic and Sub-Riemannian Flows on $V_{n,2}$ and Integrable Cases of a Heavy Rigid Body with a Gyrostat”, Regul. Chaotic Dyn., 30:5 (2025), 799–818  mathnet  crossref
  4. Andrey V. Tsiganov, “Integrable Systems on a Sphere, an Ellipsoid and a Hyperboloid”, Regul. Chaotic Dyn., 28:6 (2023), 805–821  mathnet  crossref
  5. Pavel E. Ryabov, 2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB), 2020, 1  crossref
  6. Borisov A. Mamaev I., “Rigid Body Dynamics”, Rigid Body Dynamics, de Gruyter Studies in Mathematical Physics, 52, Walter de Gruyter Gmbh, 2019, 1–520  mathscinet  isi
  7. Ol'shanskii V.Yu., “Construction of Linear Invariant Relations of Kirchhoff Equations”, Mech. Sol., 54:1 (2019), 70–80  crossref  isi  scopus
  8. Oshemkov A.A. Ryabov P.E. Sokolov S.V., “Explicit Determination of Certain Periodic Motions of a Generalized Two-Field Gyrostat”, Russ. J. Math. Phys., 24:4 (2017), 517–525  crossref  mathscinet  zmath  isi  scopus  scopus
  9. Sokolov S.V., “New Invariant Relations For One Critical Subsystem of a Generalized Two-Field Gyrostat”, Dokl. Phys., 62:12 (2017), 567–570  crossref  mathscinet  isi  scopus  scopus
  10. S.V. Sokolov, “NOVYE INVARIANTNYE SOOTNOShENIYa ODNOI KRITIChESKOI PODSISTEMY OBOBSchENNOGO DVUKhPOLEVOGO GIROSTATA, “Doklady Akademii nauk””, Doklady Akademii Nauk, 2017, no. 6, 660  crossref
  11. Mikhail P. Kharlamov, Pavel E. Ryabov, Alexander Yu. Savushkin, “Topological Atlas of the Kowalevski–Sokolov Top”, Regul. Chaotic Dyn., 21:1 (2016), 24–65  mathnet  crossref  mathscinet  zmath
  12. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Generalizations of the Kovalevskaya case and quaternions”, Proc. Steklov Inst. Math., 295 (2016), 33–44  mathnet  crossref  crossref  mathscinet  isi  elib
  13. Yehia H.M., Elmandouh A.A., “A new conditional integrable case in the dynamics of a rigid body-gyrostat”, Mech. Res. Commun., 78:A (2016), 25–27  crossref  mathscinet  isi  scopus
  14. M. P. Kharlamov, P. E. Ryabov, I. I. Kharlamova, “Topological Atlas of the Kovalevskaya–Yehia Gyrostat”, J. Math. Sci. (N. Y.), 227:3 (2017), 241–386  mathnet  mathnet  crossref  scopus
  15. Vladimir Dragović, Borislav Gajić, “Some Recent Generalizations of the Classical Rigid Body Systems”, Arnold Math J., 2:4 (2016), 511  crossref
  16. A. V. Tsyganov, “Razdelenie peremennykh dlya odnogo obobscheniya sistemy Chaplygina na sfere”, Nelineinaya dinam., 11:1 (2015), 179–185  mathnet  elib
  17. Ryabov P.E., “New Invariant Relations For the Generalized Two-Field Gyrostat”, J. Geom. Phys., 87 (2015), 415–421  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  18. A. P. Sozonov, A. V. Tsiganov, “Bäcklund transformations relating different Hamilton–Jacobi equations”, Theoret. and Math. Phys., 183:3 (2015), 768–781  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  19. P. E. Ryabov, A. Yu. Savushkin, “Fazovaya topologiya volchka Kovalevskoi – Sokolova”, Nelineinaya dinam., 11:2 (2015), 287–317  mathnet
  20. M. P. Kharlamov, P. E. Ryabov, “Topological atlas of the Kovalevskaya top in a double field”, J. Math. Sci., 223:6 (2017), 775–809  mathnet  crossref  mathscinet  elib
  21. Ol'shanskii V.Yu., “Linear invariant relations of Kirchhoff's equations”, Pmm-J. Appl. Math. Mech., 79:4 (2015), 334–349  crossref  mathscinet  isi  scopus
  22. A.V. Tsiganov, “On the Chaplygin system on the sphere with velocity dependent potential”, Journal of Geometry and Physics, 92 (2015), 94  crossref
  23. A. V. Vershilov, Yu. A. Grigorev, A. V. Tsyganov, “Ob odnoi integriruemoi deformatsii volchka Kovalevskoi”, Nelineinaya dinam., 10:2 (2014), 223–236  mathnet
  24. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Superintegrable Generalizations of the Kepler and Hook Problems”, Regul. Chaotic Dyn., 19:3 (2014), 415–434  mathnet  crossref  mathscinet  zmath
  25. Mikhail P. Kharlamov, “Extensions of the Appelrot Classes for the Generalized Gyrostat in a Double Force Field”, Regul. Chaotic Dyn., 19:2 (2014), 226–244  mathnet  crossref  mathscinet  zmath
  26. P. E. Ryabov, “Phase topology of one irreducible integrable problem in the dynamics of a rigid body”, Theoret. and Math. Phys., 176:2 (2013), 1000–1015  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  27. Yehia H.M., Elmandouh A.A., “A New Integrable Problem with a Quartic Integral in the Dynamics of a Rigid Body”, J. Phys. A-Math. Theor., 46:14 (2013), 142001  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
  28. Sokolov, VV, “Integrable quadratic classical Hamiltonians on so(4) and so(3,1)”, Journal of Physics A-Mathematical and General, 39:8 (2006), 1915  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  29. Tsiganov, AV, “A new integrable system on S-2 with the second integral quartic in the momenta”, Journal of Physics A-Mathematical and General, 38:16 (2005), 3547  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  30. Tsiganov, AV, “On a family of integrable systems on S-2 with a cubic integral of motion”, Journal of Physics A-Mathematical and General, 38:4 (2005), 921  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  31. I. Z. Golubchik, V. V. Sokolov, “Factorization of the Loop Algebra and Integrable Toplike Systems”, Theoret. and Math. Phys., 141:1 (2004), 1329–1347  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  32. A. V. Tsiganov, “Integrable Deformations of Tops Related to the Algebra $so(p,q)$”, Theoret. and Math. Phys., 141:1 (2004), 1348–1360  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  33. Tsiganov AV, Goremykin OV, “Integrable systems on so(4) related to XXX spin chains with boundaries”, Journal of Physics A-Mathematical and General, 37:17 (2004), 4843–4849  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  34. Sokolov VV, “One class of quadratic so(4) Hamiltonians”, Doklady Mathematics, 69:1 (2004), 108–111  zmath  isi
  35. Wolf T., “Applications of CRACK in the classification of integrable systems”, Superintegrability in Classical and Quantum Systems, CRM Proceedings & Lecture Notes, 37, 2004, 283–300  crossref  mathscinet  zmath  isi
  36. P. E. Ryabov, “Bifurcations of First Integrals in the Sokolov Case”, Theoret. and Math. Phys., 134:2 (2003), 181–197  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  37. V. V. Belov, S. Yu. Dobrokhotov, V. A. Maksimov, “Explicit Formulas for Generalized Action–Angle Variables in a Neighborhood of an Isotropic Torus and Their Application”, Theoret. and Math. Phys., 135:3 (2003), 765–791  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  38. Wolf, T, “Classification of integrable quadratic Hamiltonians on e(3)”, Regular & Chaotic Dynamics, 8:2 (2003), 155  mathnet  crossref  mathscinet  adsnasa  isi  scopus  scopus
  39. Komarov, IV, “Poisson maps and integrable deformations of the Kowalevski top”, Journal of Physics A-Mathematical and General, 36:29 (2003), 8035  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  40. V. V. Sokolov, A. V. Tsiganov, “Commutative Poisson Subalgebras for Sklyanin Brackets and Deformations of Some Known Integrable Models”, Theoret. and Math. Phys., 133:3 (2002), 1730–1743  mathnet  crossref  crossref  mathscinet  zmath  isi


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