The уollection

survey, 1975 - 2000 (part I)

V.V.Rumyantsev, V.S.Sergeev, S.Ya.Stepanov, A.S.Sumbatov

A.A.Dorodnitsyn Computing Centre of RAS

Vavilova, 40, Moscow, Russia

The A.A.Dorodnitsyn Computing Centre of RAS (Computing Centre of the USSR Academy of Sciences till 1991, Computing Centre of RAS since 1991 till 2001) is editing the non-periodic collections of papers (Editor-in-Chief academician of RASљ V.V.Rumyantsev). 12 issues were published during 1975-2000. In these collections there were published papers on the theory of stability and stabilisation of motion (with applications to dynamics of a rigid body and systems of bodies with rigid, solid and liquid elements, to motion of satellites, to the 3-body problem, etc.) on general and analytical mechanics, on numerical investigation methods of stability, etc. The authors of these papers are employees of the sectorљ "Theory of stability and mechanics of controlled systems" of the Department of Mechanics of the Computing Centre and also their colleagues from Moscow, Kyiv, Tiflis and Paris, students and post-graduate students of the M.V.Lomonosov Moscow State University and Moscow State Academy of Instrument Making and Computer Science. Many of papers have reviews in RJ Mechanics (USSR, Russia), Mathematical Reviews (USA) and Zentralblatt für Mathematik (Germany). This survey has 6 thematic Sections (with review of all published papers in 12 collections). Here, in this issue, two first Sections are presented:љ I. GENERAL PROBLEMS OF THE STABILITY THEORY; II. GENERAL TOPICS OF MECHANICS. Other Sections will be presented in љnext Journal issue.

There is the content of the mentioned 12 collections in the list given below. The list of all papers is presented in Appendix. In the survey the references for papers printed in the collections have the form [year of issue, the number of part (if it exists) and the order number of paper in this collection (according to the list)]. Thus, referenceљљ [1975, 4] specifies paper Rubanovskii V.N., On bifurcation and stability of stationary systems with known first integrals // Research problems of stability and stabilisation of motion. Moscow: Computing Centre of the USSR Ac. Sc., 1975, Pp. 121-200.

Appendix:

1975

1.       Van Danchzhi and Stepanov S.Ya. Stability on a finite interval of time and its numerical research. Pp. 3-58.

2.       Van Danchzhi and Stepanov S.Ya. Optimal stabilisation on a final interval of time. Pp. 59-112.

3.       Sergeev V.S. On estimation of area of attraction for asymptotically stable motions. Pp. 113-120.

4.       Rubanovskii V.N. On bifurcation and stability of stationary motions with known first integrals. Pp. 121-200.

5.       Grimailo V.I. On relative equilibrium and stability of a system of elastically coupled rigid bodies. Pp. 201-217.

1982

1.       Rubanovskii V.N. On bifurcation and stability of permanent rotations of a heavy rigid body in the case when its mass centre lays near to the principal plane of inertia. Pp. 3-55.

2.       Sergeev V.S. Construction of periodic solutions of the Euler-Poisson equations in some cases. Pp. 56-69.

3.       Samsonov ч.б. On stationary motions of a symmetric rigid body. Pp. 70-79.

4.       Sumbatov A.S. Contribution for the theorem of areas. Pp.80-86.

5.       Karapetyan A.V. On stability of stationary motions. Pp. 87-102.

6.       Dzhanikashvili G.V. On stability of some relative equilibria of a gyrostat in the restricted generalised circular 3 bodies-problem. Pp. 102-139.

7.       Nozadze G.T. On relative equilibrium of a double pendulum. Pp. 140-154.

 

 

1985

1.       Van Danchzhi. On construction of the general solution of biharmonic generalised Hill's equation and Mathieu's equation. Pp. 3-22.

2.       Karapetyan A.V. On stability of stationary motions of systems with quasi-cyclic coordinates. Pp. 23-39.

3.       Rubanovskii V.N. On stability of vertical rotations of a rigid body suspended with a rod. Pp. 40-53.

4.       Sergeev ч.у. On instability of solutions for one class of integral-differential equations in the critical case of zero root. Pp. 54-84.

5.       Stepanov S.Ya. Stationary motions of gravitated bodies. Pp. 85-89.

6.       Sulikashvili R.S. Influence of the inertia moments of the supreme orders on dynamics of a rigid body having a fixed point. Pp. 90-104.

7.       Sumbatov A.S. On the inverse problem of the calculus of variations. Pp. 105-117.

8.       Burov б.б. On partial integrals of the equations of motion of a rigid body on a frictionless horizontal plane. Pp. 118-121.

9.       Tkhai V.N. Stability of autonomous and periodic Hamilton systems. Pp. 122-151.

 

1986

1.       Burov б.б. On nonintegrability of the equations of motion of a gyroscope in the Cardano suspension. Pp. 3-10.

2.       Karapetyan A.V. and Rubanovskii V.N. On bifurcation and stability of stationary motions of a top on a horizontal plane with friction. Pp. 11-18.

3.       Rubanovskii V.N. Permanent rotations and relative equilibria of a body suspended with a rod, their bifurcation and stability. Pp. 19-34.

4.       Sergeev ч.у. On stability of equilibrium in one problem of dynamics of a rigid body. Pp. 35-46.

5.       Stepanov S.Ya. Comparison of dimensions of the domains of stability for relative equilibria of a gyrostat on a circular orbit and on the rotating Earth. Pp. 47-52.

6.       Sulikashvili R.S. On influence of terms of the highest power in the expansion of the potential of the central Newtonian attraction forces on the orientation of a rigid body on a circular orbit. Pp. 53-62.

7.       Sumbatov A.S. On motion of systems with dry friction. Pp. 63-76.

8.       Karapetyan A.V. On stability of stationary motions of systems with not uniform differential constraints. Pp. 77-85.

9.       Sergeev V.S. On instability in the critical case of zero root for integral-differential Volterra's equations. Pp. 86-92.

10.    Burov б.б. On the partial integral in the problem on motion of a heavy rigid body suspended with a rod. Pp. 93-95.

 

1987

1.       Burov б.б. On motion of a rigid body carrying the moveable mass on a spring. Pp. 3-12.

2.       Karapetyan A.V. On stability of relative equilibria of nonholonomic systems. Pp. 12-19.

3.       Rubanovskij V.N. and Mamniashvili T.I. On permanent rotations of a gyrostat suspended with a rod. Pp. 20-27.

4.       Rubanovskij V.N. and Rsymbetov K.S. On relative equilibrium of a rigid body with a flexible elastic rod on a circular orbit. Pp. 28-37.

5.       Sergeev V.S. On instability of solutions of integral-differential equations ofљ Volterra's kind in the critical case of a pair of purely imaginary roots. Pp. 38-57.

6.       Sulikashvili R.S. On stationary motions of a tetrahedron and of an octahedron in the central field of gravitation. Pp. 58-66.

7.       Sumbatov A.S. On linear integrals of linear nonconservative mechanical systems with two degrees of freedom. Pp. 67-72.

8.       Ehprikashvili G.P. On bifurcation and stability of permanent rotations of an ellipsoid of rotation on a frictionless plane. Pp. 73-82.

9.       Burov A.A. and Rubanovskii V.N. On one general solution of equations of the Kirchhoff-Clebsch type. Pp. 83-86.

 

1988

1.       Burov A.A. and Subkhankulov G.I. On some difference schemes of equations of dynamics that have the first integrals. Pp. 3-12.

2.       Karapetyan A.V. On stability of sets of not isolated stationary motions. Pp. 13-26.

3.       Nozadze G.T. On stability of vertical rotations of a rigid body suspended with a string. Pp. 27-33.

4.       Rsymbetov K.S. Stability of relative equilibrium of a rigid body with two rods on a circular orbit. Pp. 34-39.

5.       Rubanovskii V.N. On relative equilibrium of a gyrostat on a circular orbit. Pp. 40-66.

6.       Sergeev ч.у. On one case of instability for solutions of integral-differential equations. Pp. 67-81.

7.       Stepanov S.Ya. Geometrical research of opportunities to realise the one-axial equilibrium orientation of the satellite - gyrostat on a circular orbit. Pp. 82-91.

8.       Sulikashvili R.S. On stationary motions of an icosahedron and a dodecahedron in the central field of gravitation. Pp. 92-99.

9.       Sumbatov A.S. Necessary condition for onset of an impact in a system with dry friction. Pp. 100-106.

10.    Burov б.б. On partial integrals of equations of motion of a rigid body with a rotor along a frictionless horizontal plane and on one Appell's idea. Pp. 107-115.

11.    Rubanovskii V.N. and Sergeev V.S. On stationary solutions of one nonlinear diffusion problem. Pp. 116-135.

 

1991

1.       Burov б.б. On invariant relations in dynamical systems. Pp. 3-6.

1.       2. љ Isakhanova S.R. On some equilibria of floating elliptic cylinder and rectangularљљ parallelepiped. Pp. 7-17.

2.       Karapetyan A.V. Phase portraits of dissipative systems with symmetry. Pp. 18-24.

3.       Sakhokiya I.D. Libration points in the restricted circular 3 bodies-problem. Pp. 25-37.

4.       Sergeev V.S. On stability of solutions for one class of functional-differential equations. Pp. 38-47.

5.       Sosnitskii S.P.. On instability of equilibrium of natural systems. Pp. 48-61.

6.       Sumbatov A.S. On stationary rotations of a flexible shaft when dry friction forces are in supports. Pp. 62-70.

7.       Burov б.б. On motion of a body interacting with gas. Pp. 71-73.

 

1993

1.       Burov б.б. On dynamics of bodies admitting symmetries. Pp. 3-12.

2.       Isakhanova S.R. On equilibria of floating cylindrical body with any horizontal section. Pp 13-19.

3.       Karapetyan A.V. On bifurcation of stationary motions of two mutually gravitated bodies. Pp. 20-26.

4.       Rubanovskij V.N. and Rsymbetov K.S. Stability of relative equilibrium on a circular orbit of a rigid body with flexible rods. Pp. 27-44.

5.       Sergeev ч.у. On torsion of a viscoelastic bar. Pp. 45-60.

6.       Sosnitskii S.P. On stability of equilibrium of conservative systems with gyroscopic forces. Pp. 61-72.

7.       Sumbatov A.S. On the limiting equations of a plane rotary motion of a body in presence of dry friction. Pp. 73-79.

8.       Burov б.б. On invariants of evolutionary equations. Pp. 80-91.

 

1995

1.       Abrarova Ye.V. On relative equilibria of a rigid body in the central gravitational field. Pp. 3-28.

2.       Karapetyan A.V. On the trace stability of the wheeled vehicle. Pp. 29-44.

3.       Moshchevitin N.G. On the existence and smoothness of the integral of a multifrequency system of the Hamilton equations. Pp. 45-52.

4.       Naralenkova I.I. On bifurcation and stability of equilibria of a rigid body in the Newtonian field, 53-60.

5.       Sergeev V.S. On estimation of the domain of attraction for the integral-differential Volterra equations. Pp. 61-78.

6.       Stepanov S.Ya. On the algorithms of transferring a satellite-gyrostat from one stable equilibrium orientation to another. Pp. 79-88.

7.       Sumbatov A.S. On two pendula with dry friction. Pp. 89-106.

8.       Burov A.A. andљ Stepanov S.Ya. On the geometry of masses in dynamics of deformable bodies. Pp. 107-130.

9.       Zotov S.V. and Rubanovskii V.N. On equilibria of a floating cubee, their bifurcation and stability. Pp. 131-146.

10.    Abrarov D.L. Topological obstacles for integrability of the Hamilton systems of the natural type with two degrees of freedom. Application to the restricted 3-body problem. Pp. 147-173.

 

1998

1.       KarapetYan A.V. and Sitanskaya Yu.B. Invariant sets of unnatural dissipative systems. Pp. 3-17.

2.       Sergeev ч.у. On torsion of a wing. Pp. 18-28.

3.       Sergeev ч.у. On stability of equilibrium of a rotating rigid body with viscoelastic supports. Pp. 29-44.

4.       Abrarova Ye.V., Burov A.A., Stepanov S.Ya andљ Chevallier D. On equations of motion of the system tractor - semitrailer with the coupling device . Pp. 45-72.

5.       Sumbatov A.S. On motion of the n - links chain on an inclined plane. Pp. 73-84.

6.       Burov A.A. andљ Chevallier D. On reducing the order by Routh in the problems of Mechanics of a rigid body. Pp. 85-106.

7.       Grodman D.L. and Tkhai V.N. Numerical research of the periodic motions of a satellite on an elliptic orbit under the action of the gravitational moment and the moment of forces of the light pressure. Pp. 107-116.

8.       Zimovshchikov A.S. and Tkhai V.N. On stability of the triangular solutions of the unrestricted 3-body problem. Pp. 117-130.

9.       Prokonina O.V. On stability of permanent rotations of a three-axial ellipsoid on a plane with friction. Pp. 131-137.

10.    Kuleshov A.S. On permanent rotations of a heavy ellipsoid on a plane with viscous friction. Pp. 138-152.

11.    Nechayev A.N. On the relation between degrees of instability of relative equilibria and stationary motions. Pp. 153-158.

12.    Selivanova I.Yu. Stability and bifurcation of equilibria of a rigid body having a cavity filling with liquid. Pp. 159-163.

 

1999

1.       Karapetyan A.V. On permanent rotations of the Euler top under the action ofљ perturbing moments. Pp. 3-10.

2.       Sergeev V.S. On asymptotic stability in critical cases for the class of integral-differential equations. Pp. 11-32.

3.       Stepanov S.Ya. Condition of the secular and gyroscopic stability of the stationary solutions in the generalised plane 3-body problem. Pp. 33-44.

4.       Yefimov I.L. and Tkhai V.N. Stability of periodic orbits in the Hill problem. Pp. 45-60.

5.       Burov б.б. On reducing the order by Routh in the Lagrange systems. Pp. 61-65.

6.       Sumbatov A..S. Construction ofљ boundaries of the domains of stability. Pp. 66-76.

2.       7. љ Abrarova Ye.V. and Stepanov S.Ya. Solving the static indefinability of verticalљљљљљ reactions of wheels in the plane model of the system tractor - semitrailer. Pp. 77-85.

7.       Shapakidze L.O. On equilibria in the problem of liquid flow between two penetrated cylinders having different angular speeds. Pp. 86-99.

8.       Glukhikh Yu.D. and Tkhai V.N. Periodic motions of a mechanical system with one degree of freedom. Pp. 100-112.

9.       Sulikashvili R.S. On equilibria of a rigid body with a fixed point in the central Newton field. Pp. 113-120.

10.    Zimovshchikov A.S. On stability of the collinear libration points of the photogravitational elliptic restricted 3-body problem when there are two radiating bodies. Pp. 121-129.

11.    Kuleshov A.S. Supplement to dynamics of a top on a rough plane. Pp. 130-140.

12.    Lagutin I.S. Influence of dissipative and permanent moments on stability of stationary motions of a body suspended with a rod. Pp. 141-147.

13.    Nechayev A.N. On manifolds of equilibria of mechanical systems. Pp. 148-151.

14.    Prokonina O.V. On stability of permanent rotations of a top having a cavity filling with liquid. Pp. 152-158.

 

2000, Part I

1.       Seventieth anniversary ofљ R.S..Sulikashvili's birthday. Pp. 3-4.

2.       Fiftieth anniversary ofљ A.V.Karapetyan's birthday. Pp. 5-6.

3.       Sergeev V.S. On stability of equilibrium of a wing in a nonstationary flow for one case. Pp. 7-23.

4.       Pascal M. and Gagarina T. New method of dynamic simulation of elastic multi-body systems. Pp. 24-33.

5.       Sumbatov A.S. Generalised inverse matrix and its applications. Pp. 34-42.

6.       Burov б.б. On motion of a rigid body inside ideal liquid in the half-space restricted with a plane. Pp. 43-49.

7.       Cosenco I.I. Projective method of computing periodic solutions in the perturbed problems of mechanics. Pp 50-59.

8.       Tkhai V.N. Periodic motions of a heavy rigid body with one fixed point, which are close to the regular Grioli precessions. Pp. 60-67.

9.       Zimovshchikov A.S. On stability of the triangular libration points of the photogravitational elliptic restricted 3-body problem when there are two radiating bodies. Pp. 68-77.

10.    Titova N.N. Construction of the domains of the Hill stability and computation of the libration points in the photogravitational 3-body problem. Pp. 78-86.

11.    Glukhikh Yu.D., Thaj V.N. and Chevaller D.P. On stability of the permanent rotations of a heavy homogeneous ellipsoid on the absolutely rough plane. Pp. 87-104.

12.    Kuleshov A.S. On stationary motions of a heavy rigid body of rotation on the absolutely rough plane. Pp. 105-110.

13.    Kuleshov A.S. and Sitanskaya Yu.G. Stability of precessions of a gyrostat on a plane with friction. Pp. 111-118.

14.    Lagutina I.S. Influence of the dissipative and torsion moments on stability of the stationary motions of a body suspended with a rod. Pp. 119-128.

15.    Rubanovskii A.V. On stability of equilibrium of a tank with liquid which is located on a vertical elastic support. Pp. 129-149.

16.    Selyutskaya O.V. On stationary motions of the top filled with liquid. Pp. 150-156.

 

2000, Part II

1.       Abrarov D.L. On symmetries of the Hamilton systems with 3/2 degrees of freedom which are generated with the complete set of integrals. Pp. 3-28.

2.       Burov A.A. and Stepanov S.Ya. On steady motions of the plane orbital crane system. Pp. 29-39.

3.       Chevallier D.P. Dynamics from the Euler and Lagrange points of view. Pp. 40-68.

4.       Cosenco I.I. Feasibility of conditions of the theorem on the implicit function in the limiting problem for the equations of oscillations of a satellite on an elliptic orbit. Pp. 69-98.

5.       Pascal M. and Kevorkyan S. Analytical methods in the analysis of oscillations: the matrix ofљ impedance for rectangular plates. Pp. 99-111.

6.       Tkhai V.N. Parametrical resonance in the problem on stability of the collinear libration points in the photogravitational 3-body problem. Pp 112-121.

7.       Yevdokimenko A.P. On dynamics of a compound satellite on a circular orbit inљ atmosphere. Pp. 122-130.

8.       Glukhikh Yu.D. and Grikhanova T.V. On stability of the 2-periodic rotary motions of a satellite in a plane of an elliptic orbit in the spatial problem. Pp. 142-148.

9.       Tkhai V.N. and Shvygin A.L. On stability of rotations around a horizontal axis of a heavy rigid body with one fixed point. Pp. 149-157.