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Instability of periodic motions near collinear points of libration in plane restricted three- body problem examined with Liapunov theory
Equations of motion and integrals of motion derived for Sundman regularization of three- body problem
Restricted three-body problem is solved using solutions of eulers problem of two fixed centers
Nonplanar trajectory originating near Earth and passing close to Moon in restricted three-body problem
The study of resonances, unstable particles formed in particle scattering, is motivated by the questions about the strong interaction and the composition of hadrons. In order to advance this study in the intermediate energy region, a variety of techniques are used. In this thesis, we present work done on two different analyses that use the principle of unitarity and the Bethe-Salpeter equation to study the resonances Lambda(1405), Sigma(1385), and a1(1260). Firstly, we perform a simultaneous analysis of Sand P-waves of the Strangeness = -1 two-body meson-baryon scattering amplitude using all low-energy data. For the first time, differential cross section data are included for chiral unitary coupled-channel models. From this model, S- and P-wave amplitudes are extracted and we observe both well-known I(JP)=0(1/2^-) S-wave states as well as a new I(JP)=1(1/2^+) state absent in quark models and lattice QCD results. Multiple statistical and phenomenological tests suggest that, while the data clearly require an I =1 P-wave resonance, the new state just accounts for the absence of the decuplet Sigma(1385)3/2+ in the model which is subsequently included in the parameterization. Secondly, we formulate the final state interaction of the a1(1260) resonance decay in a manifestly three-body-unitary parameterization and fit it to the a1(1260) lineshape measured by the ALEPH experiment. Dalitz plots calculated from this fit are presented. The work demonstrates the feasibility to numerically solve a previously derived amplitude and its generalization to isobars with spin and coupled channels. The model is a good test case because it can also be applied to other meson decays including exotic states and modified for the finite-volume problem as it arises in lattice QCD due to its manifest unitarity. The understanding of the resonances being analyzed in both the two-body work and the three-body work gives a better understanding of intermediate energy QCD.
Series expansion for periodic orbits in restricted three-body problem according to perturbation method
Canonical elements for variables of Levi-Civita regularizing binary collisions in restricted three-body problem, noting existence of periodic orbits
Numerical analysis of librational motion of particle around lagrangian triangular point in semirestricted three-body problem
Stability of periodic orbits in elliptic restricted three body problem
Computer program for two impulse transfer in three body problem
Stability of periodic orbits in elliptic restricted three body problem
Three body gravitational capture of interstellar dust in solar system, examining zodiacal cloud
In studies of the elliptic restricted three-body problem, the true anomaly of the motion of the primaries is often used as the independent variable. The equations of motion then show invariancy in form from the circular case. It is of interest whether other independent variables exist, such that the invariant form of the equations is maintained. It is found that true anomaly is the only such variable.
Within the context of the restricted problem of three bodies the effects caused by varying the mass ratio of the primaries and the eccentricity of their orbits, upon periodic orbits of the infinitesimal mass which are numerical continuations of circular orbits in the ordinary problem of two bodies are shown. A recursive power series technique is used to numerically integrate the equations of motion as well as the first variational equations in order to generate a two parameter family of perodic orbits and identify the linear stability characteristics. Seven such families are investigated with equally spaced mass ratios from 0.0 to 1.0 and eccentricities of the orbits of the primaries in a range 0.0 to 0.6. Stable orbits are associated with large distances of the infinitesimal mass from the perturbing primary, nearly circular motion of the primaries, and small mass ratios of the primaries. Unstable orbits for the infinitesimal mass are associated with small distances from the perturbing primary, highly elliptic orbits of the primaries and large mass ratios.
The extraction of thrust from air breathing hypersonic propulsion systems is critically dependent on the degree to which chemical equilibrium is reached in the combustion process. In the combustion of H2/Air mixtures, slow three-body chemical reactions involving H-atoms, O-atoms, and the OH radical play an important role in energy extraction. A first-generation high temperature and pressure flash-photolysis/laser-induced fluorescence reactor was designed and constructed to measure these important three-body rates. The system employs a high power excimer laser to produce these radicals via the photolysis of stable precursors. A novel two-photon laser-induced fluorescence technique is employed to detect H-atoms without optical thickness or O2 absorption problems. To demonstrate the feasibility of the technique the apparatus in the program is designed to perform preliminary measurements on the H + O2 + M reaction at temperatures from 300 to 835 K.
In this paper, we examine the effects of radiation pressure, Poynting-Robertson (PR) drag, and solar wind drag on dust grains trapped in mean motion resonances with the Sun and Jupiter in the restricted (negligible dust mass) three-body Problem. We especially examine the evolution of dust grains in the 1:1 resonance. As a first step, the Sun and Jupiter are idealized to both be in circular orbit about a common center of mass (circular restricted three-body problem). From the equation of motion of the dust particle in the rotating reference frame, the drag-induced time rate of change of its Jacobi "constant," C, is then derived and expressed in spherical coordinates. This new mathematical expression in spherical coordinates shows that C, in the 1:1 resonance, both oscillates and secularly increases with increasing time. The new expression gives rise to an easy understanding of how an orbit evolves when the radiation force and solar wind drag are included. All dust grain orbits are unstable in time when PR and solar wind drag are included in the Sun-Jupiter-dust system. Tadpole orbits evolve into horseshoe orbits; and these orbits continuously expand in size to lead to close encounters with Jupiter. Permanent trapping is impossible. Orbital evolutions of a dust grain trapped in the 1:1 resonance in the planar circular, an inclined case, an eccentric case, and the actual Sun-Jupiter case are numerically simulated and compared with each other and show grossly similar time behavior. Resonances other than 1:1 are also explored with the new expression. Stable exterior resonance trapping may be possible under certain conditions. One necessary condition for such a trap is derived. Trapping in interior resonances is shown to be always unstable.
In the tractor-rocket seated-extraction candidate system for Space Shuttle Orbiter crew escape, the crewmember is pulled from his seat and away from the Orbiter via an elastic pendant, using a system of rails to guide the extraction trajectory through an opening on the window frame for flight deck crew and through the side hatch for the middeck crew. A three-body simulation has been developed to model the flight-mechanics aspects of the concept, where the three bodies are the astronaut (six DOF), the tractor rocket (six DOF), and the Shuttle Orbiter (three DOF); attention is given to crewmembers' clearance of the Orbiter structure and engine plumes.
Hodographic treatment of restricted three body problem