First order normalization in the generalized photo gravitational non-planar restricted three body problems

<p>In this paper, we normalised the second-order part of the Hamiltonian of the problem. The problem is generalised in the sense that fewer massive primary is supposed to be an oblate spheroid. By photogravitational we mean that both primaries are radiating. With the help of Mathematica, H₂ is normalised to H₂ = a₁b₁w₁ + a₂b₂w₂. The resulting motion is composed of elliptic motion with a short period (2p/w₁), completed by an oscillation along the z-axis with a short period (2p/w₂).</p>

Modeling and Analysis of Machining Force in Elliptical Vibration Cutting

Elliptical vibration cutting (EVC) is one of the main methods to use diamond tool machining of hard to cutmaterial. Accurate prediction of cutting force in elliptical vibration cutting process is not only an important basis to properly choose of cutting parameters and optimal tool geometry parameters, but also a key factor to improve the processing property of cutting. A method to build cutting force theory model in EVC is presented in this paper. Eigen decomposition of the elliptic motion locus first ,then getting the piecewise function of the cutting force model. Based on simulation analysis of the cutting force model, this paper predict the rules that vibration amplitude and angle of tool geometry affect on cutting force, which provide theory basis for choose cutting parameters and cutting tool parameter in EVC.

Averaging Tesseral Effects: Closed Form Relegation versus Expansions of Elliptic Motion

Longitude-dependent terms of the geopotential cause nonnegligible short-period effects in orbit propagation of artificial satellites. Hence, accurate analytical and semianalytical theories must cope with tesseral harmonics. Modern algorithms for dealing analytically with them allow for closed formrelegation. Nevertheless, current procedures for the relegation of tesseral effects from subsynchronous orbits are unavoidably related to orbit eccentricity, a key fact that is not enough emphasized and constrains application of this technique to small and moderate eccentricities. Comparisons with averaging procedures based on classical expansions of elliptic motion are carried out, and the pros and cons of each approach are discussed.

MOTION OF A TEST PARTICLE IN THE TRANSVERSE SPACE OF Dp-BRANES

We investigate the motion of a test particle in higher dimensions due to the presence of extended sources like Dp-branes by studying the motion in the transverse space of the brane. This is contrasted with the motion of a point particle in the Schwarzschild background in higher dimensions. Since Dp-branes are specific to 10-dimensional spacetime and exact solutions of geodesic equations for this particular spacetime has not been possible so far for the Schwarzschild background, we focus here to find the leading order solution of the geodesic equation (for motion of light rays). This enables us to compute the bending of light in both the backgrounds. We show that contrary to the well known result of no noncircular bound orbits for a massive particle, in Schwarzschild background, for d ≥ 5, the Dp-brane background does allow bound elliptic motion only for p = 6 and the perihelion of the ellipse regresses instead of advancement. We also find that circular orbits for photon are allowed only for p ≤ 3.