lower dimensional tori
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2018 ◽  
Vol 3 (1) ◽  
pp. 187-208 ◽  
Author(s):  
A. Cantero ◽  
F. Crespo ◽  
S. Ferrer

AbstractWe study the roto-orbital dynamics of a uniform sphere and a triaxial body by means of a radial intermediary, which defines a 2-DOF Hamiltonian system. Our analysis is carried out by using variables referred to the total angular momentum. Its validity and applicability is assessed numerically by experiments comprising three different scenarios; analysis of the triaxiality, eccentricity and altitude. They show that there is a range of parameters and initial conditions for which the radial distance and the slow angles are estimated accurately, even after one orbital period. On the contrary, fast angles deteriorates as the triaxiality grows. We also include the study of the relative equilibria, finding constant radius solutions filling 4-D and lower dimensional tori. These families of relative equilibria include some of the classical ones reported in the literature and some new types. For a number of scenarios the relation between the triaxiality and the inclination connected with relative equilibria are given.



2017 ◽  
Vol 37 (4) ◽  
pp. 2141-2160
Author(s):  
Xiaocai Wang ◽  
◽  
Junxiang Xu ◽  
Dongfeng Zhang ◽  


2015 ◽  
Vol 143 (1) ◽  
pp. 45-61 ◽  
Author(s):  
Xiaocai Wang ◽  
Junxiang Xu ◽  
Dongfeng Zhang


2014 ◽  
Vol 35 (7) ◽  
pp. 2311-2333 ◽  
Author(s):  
XIAOCAI WANG ◽  
JUNXIANG XU ◽  
DONGFENG ZHANG

This work focuses on the persistence of lower-dimensional tori with prescribed frequencies and singular normal matrices in reversible systems. By the Kolmogorov–Arnold–Moser theory and the special structure of unperturbed nonlinear terms in the differential equation, we prove that the invariant torus with given frequency persists under small perturbations. Our result is a generalization of X. Wang et al [Degenerate lower dimensional tori in reversible systems. J. Math. Anal. Appl.387 (2012), 776–790].





2012 ◽  
Vol 387 (2) ◽  
pp. 776-790 ◽  
Author(s):  
Xiaocai Wang ◽  
Junxiang Xu ◽  
Dongfeng Zhang


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