An algorithm for integrating stepwise the restricted problem in Thiele's coordinates
Planar restricted three body problem in Thiele coordinates, developing recurrence formulas for coefficients in Taylor series expansions of solution
Estes, R. H.↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Method for constructing periodic orbits in nonlinear dynamic systems
Method is modification of generalized Newton-Ralphson algorithm for analyzing two-point boundary problems. It constructs sequence of solutions that converge to precise dynamic solution in the sequence limit. Program calculates periodic orbits in either circular or elliptical restricted three-body problems.
Bennett, A. G.↗
Use of Green's functions in the numerical solution of two-point boundary value problems Final report, 1 Apr. 1970 - 31 Mar. 1971
Green function in solving linear and nonlinear second order ordinary differential equations including examples in finding rendezvous and periodic orbits of restricted three body system
Gallaher, L. J.↗
Regularization of vector fields by surgery
Excising neighborhood of singularity from manifold with vector field definition, making possible regularization of two and three body problems
Easton, R.↗
Calculation of trajectories utilizing a slowly-varying Jacobi function
Earth-moon and other trajectories calculation in planar elliptic restricted three body problem by slowly varying Jacobi function
Culpepper, B.↗
Measurement of C/plus/ plus e/minus/ plus e/minus/ and CO/plus/ plus e/minus/ recombination in carbon monoxide flows
Carbon ion and free electrons three body recombination rate coefficient measurement in carbon monoxide flows
Dunn, M. G.↗
Metallic ions in the equatorial ionosphere
Four positive ion composition measurements of the equatorial E region made at Thumba, India, are presented. During the day, the major ions between 90 and 125 km are NO(+) and O2(+). A metallic ion layer centered at 92 km is observed, and found to contain Mg(+), Fe(+), Ca(+), K(+), Al(+), and Na(+) ions. The layer is explained in terms of a similarly shaped latitude distribution of neutral atoms which are photoionized and charge-exchanged with NO(+) and O2(+). Three body reactions form molecular metallic ions which are rapidly lost by dissociative ion-electron recombination. Nighttime observations show downward drifting of the metallic ion layer caused by equatorial dynamo effects. These ions react and form neutral metals which exchange charges with NO(+) and O2(+) to produce an observed depletion of those ions within the metallic ion region.
Aikin, A. C.↗
Research on plasma turbulence involving binary particle collisions and collective effects
Plasmas in which binary collisions are important are studied by means of nonadiabatic methods. Two- and three-body correlations are calculated to determine the one-particle distribution for the ionization model. The general dispersion analysis is summarized, and examples of the ionization model and of the static fluctuations are discussed.
Sandri, G.↗
Kinetics of O/super 3P/ + CO + M recombination.
Measurement of rate coefficients over the temperature range from 250 to 370 K for the three-body recombination of O(super 3P) with CO. Earlier results at 300 K have been re-evaluated and were found to have been influenced by unknown impurities in the CO, which have now been removed by more elaborate purification methods. For CO as the third body, the rate constant is given by K = 6.5 x 10 to the minus 33rd exp (-4340 plus or minus 550/RT) cm to the 6th power per sq molecule per sec. For N2 and CO2, the 296 K rate constants are 2.3 and 6.2 x 10 to the minus 36th cm to the 6th power per sq molecule per sec, respectively.
Slanger, T. G.↗
Equations for the kinetic modeling of supersonically flowing electrically excited lasers
The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration-vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is then discussed.
Lind, R. C.↗
Metallic ions in the equatorial ionosphere.
Four positive ion composition measurements of the equatorial E region at Thumba, India, are presented. During the day, the major ions between 90 and 125 km are NO+ and O2+. The relative concentrations are similar to those observed at midlatitudes but exhibit unusual structural behavior with altitude. A metallic ion layer centered at 92 km is found to contain Mg+, Fe+, Ca+, K+, Al+, Na+, and possibly Si+ ions. The layer is explained in terms of a similarly shaped altitude distribution of neutral atoms that are photoionized and charge exchanged with NO+ and O2+. Three-body reactions form molecular metallic ions that are rapidly lost by dissociative ion-electron recombination.
Aikin, A. C.↗
Twilight airglow. I - Photoelectrons and forbidden O I 5577-angstrom radiation.
A payload consisting of a number of experiments to study the earth's atmosphere was launched from White Sands on Feb. 8, 1971. The differential photoelectron flux spectrum was measured as a function of altitude. The energy distribution revealed the N2 vibrational structure appearing at 2.8 V, rising to a maximum at 4 eV, decreasing to an 8-volt-wide plateau at 20 V, and then further decreasing. The ion and electron density distributions were measured simultaneously. An optical measurement of forbidden O I 5577-A radiation was made. Both electron impact on atomic oxygen and dissociative recombination of O2(+) were found to produce this emission above 150 km. The recombination rate for the O(1 S) found from a reported nightglow profile is 2.5 plus or minus 1.5 x 10 to the minus 9th cu cm/sec. Between 140 and 120 km, photodissociation is a source of 5577 radiation. Chapman three-body recombination is dominant below 120 km.
Hays, P. B.↗
Periodic solutions of a spring-pendulum system.
A study has been made of a dynamical system composed of a pendulum and a harmonic oscillator, in order to show the remarkable resemblance with many classical celestial mechanics problems, in particular, the restricted three-body problem. It is shown that the well-known investigations of periodic orbits can be applied to the present dynamics problem.
Broucke, R.↗
Periodic Trojan-type orbits in the earth-sun system
Periodic orbits about the triangular equilibrium points are found for the planar restricted three-body problem using the earth-sun system. The maximum semimajor axis for tadpole orbits ranges from the infinitesimal orbit at 1.000 AU to the near-limiting orbit at 1.00285 AU. Horseshoe orbits are found for 1.0029 to 1.0080 AU, larger horseshoes being unstable because of close approaches to the earth. Using stability tests devised by Rabe (1961, 1962), the limit of stability for nonperiodic orbits is found to occur for maximum semimajor axes near 1.0020 AU. In addition, near-periodic tadpole orbits appear to be stable against perturbations by Jupiter and Venus for periods of at least 10,000 yr. The possibility that minor planets actually exist in such orbits is considered.
Weissman, P. R.↗
Use of Green's functions in the numerical solution of two-point boundary value problems
This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.
Gallaher, L. J.↗
Optimality of incompletely measurable active and passive attitude control systems
Passive attitude control systems and active systems with incomplete state measurements are only suboptimal systems in the sense of optimal control theory, since optimal systems require complete state measurements or state estimations. An optimal system, then, requires additional hardware (especially in the case of flexible spacecraft) which results in higher costs. Therefore, it is a real engineering problem to determine how much an optimal system exceeds the suboptimal system, or in other words, what is the suboptimal system's degree of optimality. The problem will be treated in three steps: (1) definition of the degree of optimality for linear, time-invariant systems; (2) a computation method using the quadratic cost functional; (3) application to a gravity-gradient stabilized three-body satellite and a spinning flexible satellite.
Schiehlen, W.↗
Measurements of ion-molecule reactions of He/+/, H/+/, and HeH/+/ with H2 and D2
Drift tube-mass spectrometer measurements of several ion-molecule reactions believed to be prominent in the hydrogen-helium upper atmosphere of Jupiter are described. The total rate constant at 300 K of the reaction of He(+) with H2 is about 1.1 x 10 to the neg 13 cu cm/sec. The reaction proceeds mainly by dissociative charge transfer to produce H(+), with a small portion going by charge transfer to H2(+) and by atom rearrangement to HeH(+). The rate coefficient increases slowly with ion mean energy to a value of 2.8 x 10 to the neg 13 at 0.18 eV. The rate of the corresponding reaction with deuterium, He(+) + D2, has the rate coefficient of about 5 x 10 to the neg 14 at 300 K. Measurements of the three-body reaction of H' and the two-body reaction of HeH' with H2 to form H3(+) ions are described.
Johnsen, R.↗
Thermodynamics and phase separation of dense fully-ionized hydrogen-helium fluid mixtures
The free energy of a hydrogen-helium fluid mixture is evaluated for the temperatures and densities appropriate to the deep interior of a giant planet such as Jupiter. The electrons are assumed to be fully pressure-ionized and degenerate. In this regime, an appropriate first approximation to the ionic distribution functions can be found by assuming hard sphere interactions. Corrections to this approximation are incorporated by means of the perturbation theory of Anderson and Chandler. Approximations for the three-body interactions and the nonlinear response of the electron gas to the ions are included. It is predicted that a hydrogen-helium mixture, containing 10% by number of helium ions, separates into hydrogen-rich and helium-rich phases below about 8000 K, at the pressures relevant to Jupiter (4-40 Megabars). It is also predicted that the alloy occupies less volume per ion than the separated phases. The equations of state and other thermodynamic derivatives are tabulated. Implications of these results are discussed.
Stevenson, D. J.↗