An analytical approach to small amplitude solutions of the extended nearly circular Sitnikov problem

The model of extended Sitnikov Problem contains two equally heavy bodies of mass m moving on two symmetrical orbits w.r.t the centre of gravity. A third body of equal mass m moves along a line z perpendicular to the primaries plane, intersecting it at the centre of gravity. For sufficiently small distance from the primaries plane the third body describes an oscillatory motion around it. The motion of the three bodies is described by a coupled system of second order differential equations for the radial distance of the primaries r and the third mass oscillation z. This problem which is dealt with for zero initial eccentricity of the primaries motion, is generally non integrable and therefore represents an interesting dynamical system for advanced perturbative methods. In the present paper we use an original method of rewriting the coupled system of equations as a function iteration in such a way as to decouple the two equations at any iteration step. The decoupled equations are then solved by classical perturbation methods. A prove of local convergence of the function iteration method is given and the iterations are carried out to order 1 in r and to order 2 in z. For small values of the initial oscillation amplitude of the third mass we obtain results in very good agreement to numerically obtained solutions.     

云南宝兴厂金多金属矿床成矿地质条件

矿区金、铜、钼矿化与碱性斑岩相关,向阳组碎屑岩是主要矿源层及赋矿地层,北东向响水断裂控矿,近东西向次级断裂及层间断裂为储（容）矿构造。多种条件耦合成矿。     

Simulation of seismic response in an idealized city

We study the seismic response of an idealized 2D ‘city’, constituted by ten non equally-spaced, non equally-sized, homogenized blocks (i.e. buildings or groups of buildings) anchored in a soft soil layer overlying a hard halfspace. Our results display strong response inside the blocks and on the ground which qualitatively match the responses observed in some earthquake-prone cities.