This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orb...This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body＇s rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stabil- ity regions in a numerical experiment. Some stability conclu- sions are obtained. As a typical example, it is shown in detail that near circular 1 ： 2 resonant orbit is always unstable.展开更多
We study the periodic solutions of the second-order differential equations of the form where the functions, , and are periodic of period in the variable t.
We investigate the generalized polynomial Linard differential equations. Using the averaging theory of first and second order, we obtain the maximum number of limit cycles of the system.
In this paper, we investigate a third-order differential equation. Based on the averaging theory, we obtain sufficient conditions for the existence of periodic solutions to the equation.
We study the limit cycles of wide classes of perturbed Li′enard equations, which can be seen as a particular perturbation of the harmonic oscillator, using the averaging theory. We illustrate this study with many app...We study the limit cycles of wide classes of perturbed Li′enard equations, which can be seen as a particular perturbation of the harmonic oscillator, using the averaging theory. We illustrate this study with many applications.展开更多
Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y ＋ εhl1（x） ＋ ε2hl2（x）,y=-x- ε（fn1（x）y（2p＋1） ＋ gm1（x））...Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y ＋ εhl1（x） ＋ ε2hl2（x）,y=-x- ε（fn1（x）y（2p＋1） ＋ gm1（x）） ＋ ∈2（fn2（x）y（2p＋1） ＋ gm2（x））,which bifurcate from the periodic orbits of the linear center x = y,y=-x,where ε is a small parameter.The polynomials hl1 and hl2 have degree l;fn1and fn2 have degree n;and gm1,gm2 have degree m.p ∈ N and[·]denotes the integer part function.展开更多
基金partially supported by an innovation fund from Chinese academy of space technology and a grant from the Jet Propulsion Laboratory
文摘This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body＇s rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stabil- ity regions in a numerical experiment. Some stability conclu- sions are obtained. As a typical example, it is shown in detail that near circular 1 ： 2 resonant orbit is always unstable.
文摘We study the periodic solutions of the second-order differential equations of the form where the functions, , and are periodic of period in the variable t.
文摘We investigate the generalized polynomial Linard differential equations. Using the averaging theory of first and second order, we obtain the maximum number of limit cycles of the system.
文摘In this paper, we investigate a third-order differential equation. Based on the averaging theory, we obtain sufficient conditions for the existence of periodic solutions to the equation.
文摘We study the limit cycles of wide classes of perturbed Li′enard equations, which can be seen as a particular perturbation of the harmonic oscillator, using the averaging theory. We illustrate this study with many applications.
文摘Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y ＋ εhl1（x） ＋ ε2hl2（x）,y=-x- ε（fn1（x）y（2p＋1） ＋ gm1（x）） ＋ ∈2（fn2（x）y（2p＋1） ＋ gm2（x））,which bifurcate from the periodic orbits of the linear center x = y,y=-x,where ε is a small parameter.The polynomials hl1 and hl2 have degree l;fn1and fn2 have degree n;and gm1,gm2 have degree m.p ∈ N and[·]denotes the integer part function.
