This publication is cited in the following articles:
M. V. Shamolin, “Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. III. Seventh-order systems”, J. Math. Sci. (N. Y.), 291:3 (2025), 400–431
M. V. Shamolin, “Invariants of homogeneous dynamic systems of arbitrary odd order with dissipation. IV. Ninth-order systems”, J. Math. Sci. (N. Y.), 292:3 (2025), 392–427
M. V. Shamolin, “Invarianty odnorodnykh dinamicheskikh sistem proizvolnogo nechetnogo poryadka s dissipatsiei. V. Obschii sluchai”, Materialy 6 Mezhdunarodnoi konferentsii «Dinamicheskie sistemy i kompyuternye nauki: teoriya i prilozheniya» (DYSC 2024). Irkutsk, 16–20 sentyabrya 2024 g. Chast 3, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 240, VINITI, M., 2025, 49–89
M. V. Shamolin, “Invarianty odnorodnykh dinamicheskikh sistem proizvolnogo nechetnogo poryadka s dissipatsiei. I. Sistemy tretego poryadka”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXV», Voronezh, 26-30 aprelya 2024 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 236, VINITI RAN, M., 2024, 72–88
M. V. Shamolin, “Invarianty odnorodnykh dinamicheskikh sistem proizvolnogo nechetnogo poryadka s dissipatsiei. II. Sistemy pyatogo poryadka”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXV», Voronezh, 26-30 aprelya 2024 g. Chast 3, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 237, VINITI RAN, M., 2024, 49–75
M. V Shamolin, “INVARIANTS OF GEODESIC, POTENTIAL AND DISSIPATIVE SYSTEMS WITH THREE DEGREES OF FREEDOM”, Differencialʹnye uravneniâ, 60:3 (2024), 322
M. V. Shamolin, “Invariants of Geodesic, Potential, and Dissipative Systems with
Three Degrees of Freedom”, Diff Equat, 60:3 (2024), 296
M. V. Shamolin, “Tenzornye invarianty geodezicheskikh, potentsialnykh i dissipativnykh sistem. I. Sistemy na kasatelnykh rassloeniyakh dvumernykh mnogoobrazii”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 27 yanvarya — 1 fevralya 2023 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 227, VINITI RAN, M., 2023, 100–128
M. V. Shamolin, “Tenzornye invarianty geodezicheskikh, potentsialnykh i dissipativnykh sistem. II. Sistemy na kasatelnykh rassloeniyakh trekhmernykh mnogoobrazii”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 27 yanvarya — 1 fevralya 2023 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 228, VINITI RAN, M., 2023, 92–118
M. V. Shamolin, “Tenzornye invarianty geodezicheskikh, potentsialnykh i dissipativnykh sistem. III. Sistemy na kasatelnykh rassloeniyakh chetyrekhmernykh mnogoobrazii”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 27 yanvarya — 1 fevralya 2023 g. Chast 3, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 229, VINITI RAN, M., 2023, 90–119
M. V. Shamolin, “Tenzornye invarianty geodezicheskikh, potentsialnykh i dissipativnykh sistem. IV. Sistemy na kasatelnykh rassloeniyakh $n$-mernykh mnogoobrazii”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXIV», Voronezh, 3-9 maya 2023 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 230, VINITI RAN, M., 2023, 96–130
M. V. Shamolin, “Nekotorye tenzornye invarianty geodezicheskikh, potentsialnykh i dissipativnykh sistem s chetyrmya stepenyami svobody”, Chebyshevskii sb., 24:3 (2023), 190–211
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
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
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
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
M. V. Shamolin, “Nekotorye tenzornye invarianty geodezicheskikh, potentsialnykh i dissipativnykh sistem na kasatelnom rassloenii dvumernogo mnogoobraziya”, 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, 108–116
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
M. V. Shamolin, “Nekotorye tenzornye invarianty geodezicheskikh, potentsialnykh i dissipativnykh sistem na kasatelnom rassloenii trekhmernogo mnogoobraziya”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 210, VINITI RAN, M., 2022, 96–105
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
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
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
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
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
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
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
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
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
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
M. V. Shamolin, “Examples of integrable equations of motion of a five-dimensional rigid body in the presence of internal and external force fields”, J. Math. Sci. (N. Y.), 287:5 (2025), 767–803
M. V. Shamolin, “Integrable Homogeneous Dissipative Dynamical Systems of an Arbitrary Odd Order”, J Math Sci, 251:5 (2020), 760
M. V. Shamolin, “Dissipative Integrable Systems on the Tangent Bundles of $2$- and $3$-Dimensional Spheres”, Journal of Mathematical Sciences, 245:4 (2020), 498–507
M. V. Shamolin, “New Cases of Integrable Systems with Dissipation on the Tangent Bundles of a Multidimensional Manifold”, Dokl. Phys., 63:10 (2018), 424
M. V. Shamolin, “Integrable Systems with Dissipation and Two and Three Degrees of Freedom”, J Math Sci, 235:2 (2018), 220
M. V. Shamolin, “Integrable systems on the tangent bundle of a multi-dimensional sphere”, J. Math. Sci. (N. Y.), 234:4 (2018), 548–590
M. V. Shamolin, “A multidimensional pendulum in a nonconservative force field under the presence of linear damping”, Dokl. Phys., 61:9 (2016), 476
M. V. Shamolin, “New cases of integrable systems with dissipation on tangent bundles of two- and three-dimensional spheres”, Dokl. Phys., 61:12 (2016), 625
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
M. V. Shamolin, “New case of complete integrability of dynamics equations on a tangent fibering to a $3\mathrm{D}$ sphere”, Moscow University Mathematics Bulletin, 70:3 (2015), 111–114
M. V. Shamolin, “A multidimensional pendulum in a nonconservative force field”, Dokl. Phys., 60:1 (2015), 34
M. V. Shamolin, “Complete list of first integrals of dynamic equations for a multidimensional solid in a nonconservative field”, Dokl. Phys., 60:4 (2015), 183
N. V. Pokhodnya, M. V. Shamolin, “Integriruemye sistemy na kasatelnom rassloenii k mnogomernoi sfere”, Vestn. SamGU. Estestvennonauchn. ser., 2014, no. 7(118), 60–69
M. V. Shamolin, “Integrable cases in the dynamics of a multi-dimensional rigid body in a nonconservative field in the presence of a tracking force”, J. Math. Sci., 214:6 (2016), 865–891
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
M. V. Shamolin, “A new case of integrability in the dynamics of a multidimensional solid in a nonconservative field under the assumption of linear damping”, Dokl. Phys., 59:8 (2014), 375
M. V. Shamolin, “New case of integrability of dynamic equations on the tangent bundle of a 3-sphere”, Russian Math. Surveys, 68:5 (2013), 963–965
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
M. V. Shamolin, “New case of integrability in the dynamics of a multidimensional solid in a nonconservative field”, Dokl. Phys., 58:11 (2013), 496
M. V. Shamolin, “Complete list of first integrals of dynamic equations of motion of a 4D rigid body in a nonconservative field under the assumption of linear damping”, Dokl. Phys., 58:4 (2013), 143
N. V. Pokhodnya, M. V. Shamolin, “Novyi sluchai integriruemosti v dinamike mnogomernogo tela”, Vestn. SamGU. Estestvennonauchn. ser., 2012, no. 9(100), 136–150
M. V. Shamolin, “Complete list of first integrals for dynamic equations of motion of a solid body in a resisting medium with consideration of linear damping”, Moscow University Mechanics Bulletin, 67:4 (2012), 92–95
M. V. Shamolin, “A new case of integrability in spatial dynamics of a rigid solid interacting with a medium under assumption of linear damping”, Dokl. Phys., 57:2 (2012), 78
M. V. Shamolin, “A new case of integrability in the dynamics of a 4D-rigid body in a nonconservative field under the assumption of linear damping”, Dokl. Phys., 57:6 (2012), 250
M. V. Shamolin, “Novyi sluchai polnoi integriruemosti uravnenii dinamiki na kasatelnom rassloenii k trekhmernoi sfere”, Vestn. SamGU. Estestvennonauchn. ser., 2011, no. 5(86), 187–189
M. V. Shamolin, “Complete list of first integrals in the problem on the motion of a 4D solid in a resisting medium under assumption of linear damping”, Dokl. Phys., 56:9 (2011), 498
M. V. Shamolin, “A completely integrable case in the dynamics of a four-dimensional rigid body in a non-conservative field”, Russian Math. Surveys, 65:1 (2010), 183–185
V. V. Trofimov, M. V. Shamolin, “Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems”, J. Math. Sci., 180:4 (2012), 365–530
M. V. Shamolin, “Dynamical systems with variable dissipation: Approaches, methods, and applications”, J. Math. Sci., 162:6 (2009), 741–908
M. V. Shamolin, “An integrable case of dynamical equations on $so(4)\times\mathbb R^4$”, Russian Math. Surveys, 60:6 (2005), 1245–1246
