Stability of high-frequency periodic motions of a heavy rigid body with a horizontally vibrating suspension point

2016 ◽  
Vol 51 (6) ◽  
pp. 632-642
Author(s):  
M. V. Belichenko
Keyword(s):  
Rigid Body ◽  
High Frequency ◽  
Periodic Motions ◽  
Suspension Point ◽  
Heavy Rigid Body

scholarly journals On a Method of Introducing Local Coordinates in the Problem of the Orbital Stability of Planar Periodic Motions of a Rigid Body

2020 ◽  
Vol 16 (4) ◽  
pp. 581-594
Author(s):  
B.S. Bardin ◽  
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Orbital Stability ◽  
Hamiltonian Function ◽  
Periodic Motions ◽  
Autonomous Hamiltonian System ◽  
Change Of Variables ◽  
Heavy Rigid Body ◽  
Local Coordinates ◽  
Parameter Values

A method is presented of constructing a nonlinear canonical change of variables which makes it possible to introduce local coordinates in a neighborhood of periodic motions of an autonomous Hamiltonian system with two degrees of freedom. The problem of the orbital stability of pendulum-like oscillations of a heavy rigid body with a fixed point in the Bobylev – Steklov case is discussed as an application. The nonlinear analysis of orbital stability is carried out including terms through degree six in the expansion of the Hamiltonian function in a neighborhood of the unperturbed periodic motion. This makes it possible to draw rigorous conclusions on orbital stability for the parameter values corresponding to degeneracy of terms of degree four in the normal form of the Hamiltonian function of equations of perturbed motion.

scholarly journals On the motion of a heavy rigid body in two special cases of S.V.Kovalevskaya’s solution

2018 ◽  
Vol 14 (1) ◽  
pp. 123-138
Author(s):  
Г.В. Горр ◽  
◽  
Е.К. Щетинина ◽  
Keyword(s):  
Rigid Body ◽  
Heavy Rigid Body ◽  
Special Cases
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