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Runge-Kutta type formulas applied to restricted three-body problem achieving high order accuracy by m-fold differentiation and simple transformation
Integrals of motion in plane elliptic restricted three-body problems for orbits with small eccentricity near primaries
The existence of global exponential instability leading to chaos in plane (nonrigid) motions of the three-body system is demonstrated. In the presence of Newtonian attracting forces the trajectories of the three-body system in the configuration space will no longer be geodesic, and their convergence will depend on the geodesic curvature in addition to the Gaussian curvature. It is noted that the global exponential instability occurs in the n-body problem for n greater than 3 if at least two angular coordinates are disturbed, and that the chaotic instability is not necessarily accompanied by an exponential increase of the distance between the mass-points, but is associated with the exponential divergence of trajectories in the configuration space.
We investigate the two- and three-body fragmentation of tribromomethane (bromoform, CHBr 3 ) resulting from multiple ionization by 28-femtosecond near-infrared laser pulses with a peak intensity of 6 × 10 14 W cm -2 . The analysis focuses on channels consisting exclusively of ionic fragments, which are measured by coincidence momentum imaging. The dominant two-body fragmentation channel is found to be Br + + CHBr 2 +. Weaker HBr + + CBr 2 +, CHBr + + Br 2 +, CHBr 2+ + Br 2 +, and Br + + CHBr 2 2+ channels, some of which require bond rearrangement prior to or during the fragmentation, are also observed. The dominant three-body fragmentation channel is found to be Br + + Br + + CHBr + . This channel includes both concerted and sequential fragmentation pathways, which we identify using the native frames analysis method. We compare the measured kinetic energy release and momentum correlations with the results of classical Coulomb explosion simulations and discuss the possible isomerization of CHBr 3 to BrCHBr–Br (iso-CHBr 3 ) prior to the fragmentation.
Numerous unexpected operational issues relating to the abrasive nature of lunar dust, such as scratched visors and spacesuit pressure seal leaks, were encountered during the Apollo missions. To avoid reoccurrence of these unexpected detrimental equipment problems on future missions to the Moon, a series of two- and three-body abrasion tests were developed and conducted in order to begin rigorously characterizing the effect of lunar dust abrasiveness on candidate surface system materials. Two-body scratch tests were initially performed to examine fundamental interactions of a single particle on a flat surface. These simple and robust tests were used to establish standardized measurement techniques for quantifying controlled volumetric wear. Subsequent efforts described in the paper involved three-body abrasion testing designed to be more representative of actual lunar interactions. For these tests, a new tribotester was developed to expose samples to a variety of industrial abrasives and lunar simulants. The work discussed in this paper describes the three-body hardware setup consisting of a rotating rubber wheel that applies a load on a specimen as a loose abrasive is fed into the system. The test methodology is based on ASTM International (ASTM) B611, except it does not mix water with the abrasive. All tests were run under identical conditions. Abraded material specimens included poly(methyl methacrylate) (PMMA), hardened 1045 steel, 6061-T6 aluminum (Al) and 1018 steel. Abrasives included lunar mare simulant JSC- 1A-F (nominal size distribution), sieved JSC-1A-F (<25 m particle diameter), lunar highland simulant NU-LHT-2M, alumina (average diameter of 50 m used per ASTM G76), and silica (50/70 mesh used per ASTM G65). The measured mass loss from each specimen was converted using standard densities to determine total wear volume in cm3. Abrasion was dominated by the alumina and the simulants were only similar to the silica (i.e., sand) on the softer materials of aluminum and PMMA. The nominal JSC- 1A-F consistently showed more abrasion wear than the sieved version of the simulant. The lunar dust displayed abrasivity to all of the test materials, which are likely to be used in lunar landing equipment. Based on this test experience and pilot results obtained, recommendations are made for systematic abrasion testing of candidate materials intended for use in lunar exploration systems and in other environments with similar dust challenges.
Three body problem by hamilton-jacobi perturbation theory - guidance systems
A detailed theoretical analysis of the three-body effects in the putative planetary system of PSR 1257+12 is presented. Ways in which these effects are manifested in the pattern of pulse arrival times are discussed; the dominant perturbation is described as a modulation of the phases of the near-sinusoidal signals of the two planetary companions. Explicit formulas for the time dependence of the oscillating orbital elements that are needed for an improved timing model for this system are provided. If a timing model with fixed, independent Keplerian orbits continues to be used for the timing analysis, and if two planets are indeed orbiting this pulsar, then the three-body effects should become detectable by means of a growth in the postfit residuals as more observations are accumulated. If the typical error in the pulse arrival time measurements is about 10 microsec, the amplitude of the postfit residuals will increase beyond this level with three to five years of timing observations.
Disentangling sequential and concerted three-body fragmentation has been a longstanding endeavor in studies of molecular dynamics. To accomplish this goal, we recently introduced a novel method to separate sequential from concerted breakup, where the sequential events are analyzed in their native frames [J. Rajput et al., Phys. Rev. Lett. 120, 103001 (2018)]. The essence of this method is the use of the Jacobi coordinates' conjugate momenta to reduce the dimensionality of the multibody fragmentation in combination with a clear signature for sequential breakup. To demonstrate this method, we employ coincidence momentum imaging to study the strong-field dissociative ionization of OCS into O + +C + + S + , which typically undergoes concerted fragmentation or sequential breakup involving either a metastable CO 2+ or CS 2+ molecule. We identify sequential breakup using a uniform distribution as a function of the angle between the conjugate momenta, associated with the first and second fragmentation steps, which is due to the rotation of the intermediate molecule in the fragmentation plane. Furthermore, by exploiting this uniform distribution, we separate the sequential and concerted distributions in any plot created from the measured momenta.
Perturbation technique to study three-body problem of motion of close satellite
Perturbation technique to study three-body problem of motion of close satellite
Trajectory computation technique for three-body motion is based on analytical derivation and empirical validation of pseudostate theory. Application of technique yields ''overlapped conic'' trajectories with error magnitudes only 20 percent as great as those of patched conic trajectories.
Periodic orbit families in planar Pythagorean three body problem
A description is given of some properties of the characteristic exponents of the general three-body problem. The variational equations on which the analysis is based are obtained by linearizing the Lagrangian equations of motion in the neighborhood of a given known solution. Attention is given to the fundamental matrix of solutions, the characteristic equation, the three trivial solutions of the variational equations of the three-body problem, symmetric periodic orbits, and the half-period properties of symmetric periodic orbits.
Existance of periodic solutions passing near both masses of the restricted three-body problem
Determination and survey of periodic trojan orbits in the restricted problem of three bodies
Simultaneous removal of singularities of plane circular restricted three-body problem by coordinate transformation defined by conformal mapping
Self-consistent three-body calculation of pion- nucleon scattering using off-energy shell theory
Application of Krylov-Bogolubov method to solution of stellar three-body problem