Access the full text.
Sign up today, get DeepDyve free for 14 days.
A. Markeyev (2002)
An algorithm for normalizing Hamiltonian systems in the problem of the orbital stability of periodic motionsJournal of Applied Mathematics and Mechanics, 66
H. Poincaré, R. Magini (1899)
Les méthodes nouvelles de la mécanique célesteIl Nuovo Cimento (1895-1900), 10
A.P. Markeev (2016)
On the Stability of the Two-Link Trajectory of a Parabolic Birkhoff BilliardNelin. Dinam., 12
F.R. Gantmacher (1975)
Lectures in Analytical Mechanics
A. Martyniuk, B. Radzishevskii (1977)
Theory of stability of motion, 22
(2005)
On the Steklov Case in Rigid Body Dynamics, Regul
A. Markeev (2016)
On the stability of the two-link trajectory of the parabolic Birkhoff billiardsNonlinear Dynamics, 12
(1978)
Libration Points in Celestial Mechanics and Space Dynamics, Moscow: Nauka, 1978 (Russian)
(2003)
On Stability of Regular Precessions of a Non-Symmetric Gyroscope
(1975)
Lectures in Analytical Mechanics, Moscow: Mir
A. Markeev (2008)
The dynamics of a rigid body colliding with a rigid surfaceRegular and Chaotic Dynamics, 13
A.P. Markeev (2005)
On the Steklov Case in Rigid Body DynamicsRegul. Chaotic Dyn., 10
V. Arnold, V. Kozlov, A. Neishtadt (1997)
Mathematical aspects of classical and celestial mechanics (2nd ed.)
A.P. Markeev (1978)
Libration Points in Celestial Mechanics and Space Dynamics
G.D. Birkhoff (1966)
Dynamical Systems
The problem of orbital stability of a periodic motion of an autonomous two-degreeof- freedom Hamiltonian system is studied. The linearized equations of perturbed motion always have two real multipliers equal to one, because of the autonomy and the Hamiltonian structure of the system. The other two multipliers are assumed to be complex conjugate numbers with absolute values equal to one, and the system has no resonances up to third order inclusive, but has a fourth-order resonance. It is believed that this case is the critical one for the resonance, when the solution of the stability problem requires considering terms higher than the fourth degree in the series expansion of the Hamiltonian of the perturbed motion.
Regular and Chaotic Dynamics – Springer Journals
Published: Feb 22, 2018
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.