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Vershik A.M., Faddeev L.D. Differential geometry and Lagrangian mechanics with constraints.-Dokl. Akad. Nauk SSSR 202:3 (1972), 555–557 = Soviet Physics Doklady 17:1 (1972), 34–36.
Vershik A.M., Faddeev L.D. Lagrangian mechanics in invariant form.-In: Problems of Theoretical Physics. vol.2, Leningrad, 1975 = Selecta Math. Sov. 1:4 (1981), 339–350.
Godbillon C. Géométrie différentielle et méchanique analytique. Hermann, Paris, 1969.
Arnold V.I. Mathematical Methods of Classical Mechanics, Springer-Verlag, New York, 1980.
Vershik A.M. Several remarks on infinite-dimensional problems of linear programming.-Usp. Mat. Nauk 25:5 (1970), 117–124.
Vershik A.M., Chernjakov A.G. Fields of convex polytops and Pareto-Smale optimum.-In: Optimization, Novosibirsk, 1982. (To be publish in Selecta Mathematica Sovietica).
Chaplygin S.A. Studies on Dynamics of Non-Holonomic Systems, Moscow, 1949 (in Russian).
Dobronravov V.V. Foundations of Mechanics of Non-Holonomic Systems, Moscow, 1970 (in Russian).
Neimark I.I., Fufaev N.A. Dynamics of Non-Holonomic Systems, Moscow, 1967 (in Russian).
Gohman A.V. Differential-Geometric Foundations of the Classical Dynamics of Systems, Saratov, 1969 (in Russian).
Ter-Krikorov A.M. Optimal Control and Mathematical Economics, Moscow, 1977 (in Russian).
Novikov S.P. Variational methods and periodic solutions of the Kirchhoff type equations.-Funct. Anal. Appl. 15:4 (1981).
Kobayashi S., Nomizu K. Foundations of Differential Geometry, vol. 1, Interscience, New York, 1963.
Busemann H. The Geometry of Geodesics, Academic Press, New York, 1955.
Manakov S.V. Remarks on integrating the Euler equations of dynamics of n-dimensional rigid body.-Funct. Anal. Appl. 10:4(1976)
Mistchenko A.S., Fomenko A.T. Generalized Liouville's method of integrating Hamiltonian systems.-Funct. Anal. Appl. 12:2 (1978).
Alekseev V.M., Tihomirov V.M., Fomin S.V. Optimal Control, Moscow, 1981 (in Russian).
Bishop R.L., Crittenden R.J. Geometry of Manofolds, Academic Press, New York, 1964.
Stenberg S. Lectures on differental geometry. N.J., 1964.
Perelomov A. Integrable systems of classical mechanic and Lie algebras. Systems with constraints. ITEP-116, preprint, Moscow, 1983 (in Russian).
Gershkovich V. Twoside estimations of a metric which generated by absolutely nonholonomic distribution on a Riemanian manifold. Soviet Doklady, 1984.
Vershik A., Chernjakov A. Critical points of fields of convex polytopes and the Pareto-Smale optimum with respect to a convex cone. Soviet Math. Dokl. Vol. 26 (1982), No.2.
Gliklikh Yu. Riemanian parallel translation in nonlinear mechanics. See this volume.
Smirnov V. A course of higher mathematics. Vol. IV, p.1, Moscow, 1974 (in Russian).
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Vershik, A.M. (1984). Classical and non-classical dynamics with constraints. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis — Studies and Applications I. Lecture Notes in Mathematics, vol 1108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099563
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DOI: https://doi.org/10.1007/BFb0099563
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