Variable mass motion in the Hénon–Heiles system

In this work, we analyze the motion properties of the test particle, that has a variable mass within the frame of Hénon–Heiles system. We derive the equations of motion of the test particle which varies its mass according to Jean’s law. We also determine the quasi-Jacobi integral which shows the effective variation due to variable mass parameters. Further, we studied the locations of stationary points and their stability, after using Meshcherskii spacetime inverse transformations.

Minimal velocity surface in the restricted circular Three-Body-Problem

In the framework of the restricted circular Three-Body-Problem, the concept of the minimum velocity surface S is introduced, which is a modification of the zero-velocity surface (Hill surface). The existence of Hill surface requires occurrence of the Jacobi integral. The minimum velocity surface, other than the Jacobi integral, requires conservation of the sector velocity of a zero-mass body in the projection on the plane of the main bodies motion. In other words, there must exist one of the three angular momentum integrals. It is shown that this integral exists for a dynamic system obtained after a single averaging of the original system by longitude of the main bodies. Properties of S are investigated. Here is the most significant. The set of possible motions of the zero-mass body bounded by the surface S is compact. As an example the surfaces S for four small moons of Pluto are considered in the framework of the averaged problem Pluto — Charon — small satellite. In all four cases, S represents a topological torus with small cross section, having a circumference in the plane of motion of the main bodies as the center line.

Heterogeneous Oblate Primaries in Photo-gravitational CR5BP with Kite Configuration

This paper presents the investigation of the motion of infinitesimal body in the circular restricted five-body problem in which four bodies are taken as heterogeneous oblate spheroid with different densities in three layers and sources of radiation pressure. These four primaries are moving on the circumference of a circle and form a kite configuration. After evaluating the equations of motion and Jacobi-integral, we study the numerical part of the paper such as equilibria, zero-velocity curves and regions of motion. Finally, we examine the stability of the equilibria and observed that all the equilibria are unstable.