RUS  ENG
Full version
JOURNALS // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1996, Number 4, Pages 57–69 (Mi vmumm2036)

An introduction to the problem of the braking of a body in a resisting medium, and a new two-parameter family of phase portraits
M. V. Shamolin

This publication is cited in the following articles:
  1. M. V. Shamolin, “Integriruemye dinamicheskie sistemy nechetnogo poryadka s dissipatsiei raznogo znaka”, Tr. sem. im. I. G. Petrovskogo, 33, Izdatelstvo Moskovskogo universiteta, M., 2023, 424–464  mathnet
  2. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii trekhmernogo mnogoobraziya”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 205, VINITI RAN, M., 2022, 22–54  mathnet  crossref
  3. M. V. Shamolin, “Sistemy s chetyrmya stepenyami svobody s dissipatsiei: analiz i integriruemost”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 205, VINITI RAN, M., 2022, 55–94  mathnet  crossref
  4. M. V. Shamolin, “Sistemy s pyatyu stepenyami svobody s dissipatsiei: analiz i integriruemost. I. Porozhdayuschaya zadacha iz dinamiki mnogomernogo tverdogo tela, pomeschennogo v nekonservativnoe pole sil”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXXII», Voronezh, 3–9 maya 2021 g.  Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 208, VINITI RAN, M., 2022, 91–121  mathnet  crossref
  5. M. V. Shamolin, “Sistemy s pyatyu stepenyami svobody s dissipatsiei: analiz i integriruemost. II. Dinamicheskie sistemy na kasatelnykh rassloeniyakh”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXXII», Voronezh, 3–9 maya 2021 g.  Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 209, VINITI RAN, M., 2022, 88–107  mathnet  crossref
  6. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii chetyrekhmernogo mnogoobraziya. I. Uravneniya geodezicheskikh”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 210, VINITI RAN, M., 2022, 77–95  mathnet  crossref
  7. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii chetyrekhmernogo mnogoobraziya. II. Potentsialnye silovye polya”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 211, VINITI RAN, M., 2022, 29–40  mathnet  crossref
  8. M. V. Shamolin, “Sistemy s konechnym chislom stepenei svobody s dissipatsiei: analiz i integriruemost. I. Porozhdayuschaya zadacha iz dinamiki mnogomernogo tverdogo tela, pomeschennogo v nekonservativnoe pole sil”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 211, VINITI RAN, M., 2022, 41–74  mathnet  crossref
  9. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii chetyrekhmernogo mnogoobraziya. III. Silovye polya s dissipatsiei”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 212, VINITI RAN, M., 2022, 120–138  mathnet  crossref
  10. M. V. Shamolin, “Sistemy s konechnym chislom stepenei svobody s dissipatsiei: analiz i integriruemost. II. Obschii klass dinamicheskikh sistem na kasatelnom rassloenii mnogomernoi sfery”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 212, VINITI RAN, M., 2022, 139–148  mathnet  crossref
  11. M. V. Shamolin, “Sistemy s konechnym chislom stepenei svobody s dissipatsiei: analiz i integriruemost. III. Sistemy na kasatelnykh rassloeniyakh gladkikh $n$-mernykh mnogoobrazii”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 213, VINITI RAN, M., 2022, 96–109  mathnet  crossref
  12. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii gladkogo konechnomernogo mnogoobraziya. I. Uravneniya geodezicheskikh na kasatelnom rassloenii gladkogo $n$-mernogo mnogoobraziya”, Algebra, geometriya i kombinatorika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 214, VINITI RAN, M., 2022, 82–106  mathnet  crossref  mathscinet
  13. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii gladkogo konechnomernogo mnogoobraziya. II. Uravneniya dvizheniya na kasatelnom rassloenii k $n$-mernomu mnogoobraziyu v potentsialnom silovom pole”, Algebra, geometriya i kombinatorika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 215, VINITI RAN, M., 2022, 81–94  mathnet  crossref
  14. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii gladkogo konechnomernogo mnogoobraziya. III. Uravneniya dvizheniya na kasatelnom rassloenii k $n$-mernomu mnogoobraziyu v silovom pole s peremennoi dissipatsiei”, Algebra, geometriya, differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 216, VINITI RAN, M., 2022, 133–152  mathnet  crossref
  15. M. V. Shamolin, “Sluchai integriruemykh dinamicheskikh sistem proizvolnogo nechetnogo poryadka s dissipatsiei”, Materialy mezhdunarodnoi konferentsii po matematicheskomu modelirovaniyu v prikladnykh naukakh “International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19”. Belgorod, 20–24 avgusta 2019 g., Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 195, VINITI RAN, M., 2021, 142–156  mathnet  crossref
  16. M. V. Shamolin, “Integriruemye odnorodnye dinamicheskie sistemy s dissipatsiei na kasatelnom rassloenii dvumernogo mnogoobraziya”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 202, VINITI RAN, M., 2021, 43–69  mathnet  crossref
  17. M. V. Shamolin, “Semeistva portretov klassov dinamicheskikh sistem mayatnikovogo tipa”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 202, VINITI RAN, M., 2021, 70–98  mathnet  crossref
  18. M. V. Shamolin, “Nekotorye integriruemye neavtonomnye dinamicheskie sistemy s dissipatsiei”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 202, VINITI RAN, M., 2021, 99–113  mathnet  crossref
  19. M. V. Shamolin, “Ob ustoichivosti reshenii dinamicheskikh sistem s dissipatsiei”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 202, VINITI RAN, M., 2021, 114–125  mathnet  crossref
  20. M. V. Shamolin, “Topograficheskie sistemy Puankare i sistemy sravneniya malykh i vysokikh poryadkov”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 50–67  mathnet  crossref  mathscinet
  21. M. V. Shamolin, “Sluchai integriruemykh dinamicheskikh sistem devyatogo poryadka s dissipatsiei”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 68–81  mathnet  crossref  mathscinet
  22. M. V. Shamolin, “Predelnye mnozhestva differentsialnykh uravnenii okolo singulyarnykh osobykh tochek”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 119–128  mathnet  crossref  mathscinet
  23. M. V. Shamolin, “Integrable variable dissipation systems on the tangent bundle of a multi-dimensional sphere and some applications”, J. Math. Sci., 230:2 (2018), 185–353  mathnet  crossref  elib
  24. M. V. Shamolin, “Rigid body motion in a resisting medium modelling and analogues with vortex streets”, Math. Models Comput. Simul., 7:4 (2015), 389–400  mathnet  crossref  elib
  25. M. V. Shamolin, “Some classes of integrable problems in spatial dynamics of a rigid body in a nonconservative force field”, J. Math. Sci. (N. Y.), 210:3 (2015), 292–330  mathnet  crossref
  26. N. V. Pokhodnya, M. V. Shamolin, “Nekotorye usloviya integriruemosti dinamicheskikh sistem v transtsendentnykh funktsiyakh”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 9/1(110), 35–41  mathnet
  27. V. V. Trofimov, M. V. Shamolin, “Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems”, J. Math. Sci., 180:4 (2012), 365–530  mathnet  crossref  mathscinet
  28. M. V. Shamolin, “Dynamical systems with variable dissipation: Approaches, methods, and applications”, J. Math. Sci., 162:6 (2009), 741–908  mathnet  crossref  mathscinet  zmath  elib  elib


© Steklov Math. Inst. of RAS, 2025