A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consi...A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.展开更多
By means of theory of topological degree in nonlinear functional analysiscombining with qualitative analysis in ordinary differential equations, we discuss theexistence of nontrivial periodic orbits to a higher di...By means of theory of topological degree in nonlinear functional analysiscombining with qualitative analysis in ordinary differential equations, we discuss theexistence of nontrivial periodic orbits to a higher dimensional autonomous system witha non-hyperbolic singular point.展开更多
The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,...The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,9] and the eccentricity e ∈ [0,1）.In this paper we use Maslov-type index to study the stability of these solutions and prove that the elliptic Lagrangian solutions is hyperbolic for β ＆gt; 8 with any eccentricity.展开更多
Using variational minimizing methods,we prove the existence of the odd symmetric parabolic or hyperbolic orbit for the restricted 3-body problems with weak forces.
For general first-order quasilinear hyperbolic systems,based on the analysis of simple wave solutions along characteristic trajectories,the global two-sided exact boundary controllability is achieved in a relatively s...For general first-order quasilinear hyperbolic systems,based on the analysis of simple wave solutions along characteristic trajectories,the global two-sided exact boundary controllability is achieved in a relatively short controlling time.展开更多
基金Projects(NZ2013303,NZ2014201)supported by the National Natural Science Foundation of ChinaProjects(51375226,51305196,51475226)supported by the Fundamental Research Funds for the Central Universities,China
文摘A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.
文摘By means of theory of topological degree in nonlinear functional analysiscombining with qualitative analysis in ordinary differential equations, we discuss theexistence of nontrivial periodic orbits to a higher dimensional autonomous system witha non-hyperbolic singular point.
基金supported by National Natural Science Foundation of China (Grant No.11131004)
文摘The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,9] and the eccentricity e ∈ [0,1）.In this paper we use Maslov-type index to study the stability of these solutions and prove that the elliptic Lagrangian solutions is hyperbolic for β ＆gt; 8 with any eccentricity.
基金supported by National Natural Science Foundation of China (Grant No. 11071175)a grant for advisor and PhD students from educational committee of China
文摘Using variational minimizing methods,we prove the existence of the odd symmetric parabolic or hyperbolic orbit for the restricted 3-body problems with weak forces.
基金supported by the National Natural Science Foundation of China(Nos.1132615911401421)+2 种基金Shanghai Key Laboratory for Contemporary Applied Mathematics,Fudan Universitythe Initiative Funding for New Researchers,Fudan UniversityYang Fan Foundation of Shanghai on Science and Technology(No.15YF1401100)
文摘For general first-order quasilinear hyperbolic systems,based on the analysis of simple wave solutions along characteristic trajectories,the global two-sided exact boundary controllability is achieved in a relatively short controlling time.
