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References
|
|
[1] |
Beletskii, V. V., Motion of an Artificial Satellite about Its Center of Mass, Jerusalem, 1966, x, 261 pp. |
[2] |
Beletskii, V. V., Satellite's Motion about Center of Mass in a Gravitational Field, MGU, Moscow, 1975 (Russian) |
[3] |
Markeev, A. P., Linear Hamiltonian Systems and Some Problems of Stability of the Satellite Center of Mass, R&C Dynamics, Institute of Computer Science, Izhevsk, 2009, 396 pp. (Russian) |
[4] |
Korteweg, D. J., “Sur certaines vibrations d'ordre supérieur et d'intensité anormale — vibrations de relations, — dans les mécanismes à plusieurs degrés de liberté”, Arch. Néerl. sci. exactes et natur. Sér. 2, 1 (1898), 229–260 |
[5] |
Beth, H. I. E., “Les oscillations autour d'une position dans le cas d'existence d'une relation linéaire simple entre les nombres vibratoires”, Arch. Néerl. sci. exactes et natur. Sér. 2, 15 (1910), 246–283 |
[6] |
Beth, H. I. E., “Les oscillations autour d'une position dans le cas d'existence d'une relation linéaire simple entre les nombres vibratoires (suite)”, Arch. Néerl. sci. exactes et natur. Sér. 3A, 1 (1912), 185–213 |
[7] |
Markeyev, A. P., “Non-Linear Oscillations of a $1:1$ Resonance Hamiltonian System”, J. Appl. Math. Mech., 75:6 (2011), 631–646 ; Prikl. Mat. Mekh., 75:6 (2011), 901–922 (Russian) |
[8] |
Hénon, M. and Heiles, C., “The Applicability of the Third Integral of Motion: Some Numerical Experiments”, Astronom. J., 69:1 (1964), 73–79 |
[9] |
Roels, J., “An Extension to Resonant Cases of Liapunov's Theorem Concerning the Periodic Solutions near a Hamiltonian Equilibrium”, J. Differential Equations, 9:2 (1971), 300–324 |
[10] |
Braun, M., “On the Applicability of the Third Integral of Motion”, J. Differential Equations, 13:2 (1973), 300–318 |
[11] |
Breiter, S. and Elipe, A., “Pseudo-Oscillator with a Quartic Perturbation”, Mech. Res. Comm., 28:2 (2001), 119–126 |
[12] |
Kholostova, O. V. and Safonov, A. I., “Investigation of the Motions of an Autonomous Hamiltonian System at a $1:1$ Resonance”, Regul. Chaotic Dyn., 22:7 (2017), 792–807 |
[13] |
Birkhoff, G. D., Dynamical Systems, AMS, Providence, R.I., 1966, 305 pp. |
[14] |
Giacaglia, G. E. O., Perturbation Methods in Non-Linear Systems, Appl. Math. Sci., 8, Springer, New York, 1972, viii+369 pp. |
[15] |
Markeyev, A. P., “The Critical Case of a Pair of Zero Roots in a Two-Degree-of-Freedom Hamiltonian System”, J. Appl. Math. Mech., 62:3 (1998), 341–349 ; Prikl. Mat. Mekh., 62:3 (1998), 372–382 (Russian) |
[16] |
Markeev, A. P., “On Stability and Non-Linear Oscillations of Hamiltonian System in a Resonant Case”, Mech. Solids, 33:4 (1998), 32–41; Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, 1998, no. 4, 38–49 (Russian) |
[17] |
Arnol'd, V. I., Kozlov, V. V., and Neĭshtadt, A. I., Mathematical Aspects of Classical and Celestial Mechanics, Encyclopaedia Math. Sci., 3, 3rd ed., Springer, Berlin, 2006, xiv+518 pp. |
[18] |
Markeev, A. P., “Nonlinear Oscillations of Sympathetic Pendulums”, Nelin. Dinam., 6:3 (2010), 605–621 (Russian) |
[19] |
Markeyev, A. P., “An Algorithm for Normalizing Hamiltonian Systems in the Problem of the Orbital Stability of Periodic Motions”, J. Appl. Math. Mech., 66:6 (2002), 889–896 ; Prikl. Mat. Mekh., 66:6 (2002), 929–938 (Russian) |
[20] |
Neishtadt, A. I., “Estimates in the Kolmogorov Theorem on Conservation of Conditionally Periodic Motions”, J. Appl. Math. Mech., 45:6 (1981), 766–772 ; Prikl. Mat. Mekh., 45:6 (1981), 1016–1025 (Russian) |