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At least 649 records · Page 36

A note on obtaining an approximate value for the period of a periodic solution of x-double prime = -V prime /x/

The first integral of x-double prime = - V prime (x) yields an integral for the period of a periodic solution, if such exists. In general, this integral cannot be evaluated. By means of an approximate solution along with the minimization of a mean-square error, one can obtain an approximate value for the period in terms of the amplitude of the motion. The calculated period agrees very well with the period obtained by means of numerical integration for the case of orbit-orbit resonance involving the motion of two satellites of a planet. The same method is applied to obtain an alternative derivation of the first Krylov-Bogoliuboff averaging method in nonlinear mechanics.

Lass, H.↗

Abort separation study of a shuttle orbiter and external tank at hypersonic speeds

The effects of several parameters on the relative motions of a space shuttle orbiter design and its external tank were determined during staging for the return-to-launch-site abort mode. The parameters included angle of attack, dynamic pressure, flight-path angle, pitch rate, elevon effectiveness and the use of thrust applied to the tank. The relative positions of each component were determined by a separation trajectory computer program which incorporated data obtained in wind-tunnel tests with the orbiter and tank in proximity. These tests were conducted at Mach 10.3 in a continuous-flow hypersonic tunnel. All separation cases were initiated at a constant Mach number of 10 with an assumed sideslip angle of 0 deg.

Bernot, P. T.↗

Binary Orbits as the Driver of Gamma-Ray Emission and Mass Ejection in Classical Novae

Classical novae are the most common astrophysical thermonuclear explosions, occurring on the surfaces of white dwarf stars accreting gas from companions in binary star systems. Novae typically expel about 10 (sup -4) solar masses of material at velocities exceeding 1,000 kilometers per second.However, the mechanism of mass ejection in novae is poorly understood, and could be dominated by the impulsive flash of thermonuclear energy, prolonged optically thick winds or binary interaction with the nova envelope. Classical novae are now routinely detected at giga-electronvolt gamma-ray wavelengths, suggesting that relativistic particles are accelerated by strong shocks in the ejecta. Here we report high-resolution radio imaging of the gamma-ray-emitting nova V959 Mon. We find that its ejecta were shaped by the motion of the binary system: some gas was expelled rapidly along the poles as a wind from the white dwarf, while denser material drifted out along the equatorial plane, propelled by orbital motion..At the interface between the equatorial and polar regions, we observe synchrotron emission indicative of shocks and relativistic particle acceleration, thereby pinpointing the location of gamma-ray production. Binary shaping of the nova ejecta and associated internal shocks are expected to be widespread among novae, explaining why many novae are gamma-ray emitters.

binary orbits as the driver of gamma-ray↗

Investigations of Relations Between Jupiter-Europa and Jupiter-Ganymede Resonant Tori in the Planar Bicircular Restricted 4-Body Problem

Most unstable periodic orbits of the planar circular restricted 3-body problem (PCRTBP) persist as invariant tori when a periodic forcing is added to the equations of motion. Among the persisting orbits are unstable resonant periodic or- bits. In this study, we first compute invariant tori in the planar concentric cir- cular restricted 4-body problem corresponding to exterior Jupiter-Europa and in- terior Jupiter-Ganymede PCRTBP resonant periodic orbits. Motivated by the 2:1 Laplace resonance between the orbits of Europa and Ganymede around Jupiter, we then use the computed tori to characterize relations between m:n Jupiter-Ganymede and m:2n Jupiter-Europa PCRTBP resonant orbits.

de la Llave, Rafael↗

Dynamics of Drag Free Formations in Earth Orbit

In this paper the translational equations of motion of a formation of n spacecraft in Earth orbit, n(sub f) of which are drag-free spacecraft, are derived in a coordinate-free manner using the balance of linear momentum and direct tensor notation. A drag-free spacecraft consists of a spacecraft bus and a proof mass shielded from external disturbances in an internal cavity. By controlling the spacecraft so that the proof mass remains centered in the cavity, the spacecraft follows a purely gravitational orbit. The results described in this paper provide a first step toward coupling drag-free control technology with formation flying in order to mitigate the effect of differential aerodynamic drag on formation flying missions (e.g., Earth imaging applications) in low Earth orbit.

drag-free technology↗

Models of Earth's Atmosphere (120 to 1000 Km)

Atmospheric conditions encountered by a spacecraft in orbit about the Earth are important factors in space vehicle design, mission planning, and mission operations. Density is the primary atmospheric property that affects the spacecraft's orbital altitude, lifetime, and motion in the altitude range of 120 to 1000 kilometers. Near the lower limit of this range where density is greatest, a spacecraft will generally remain in orbit for a very short time; near the upper limit, the density effect on orbital lifetime is almost negligible. Density directly affects the torques which result from aerodynamic interaction between the space vehicle and the atmosphere; such torques must be considered in design of spacecraft attitude control systems. Density scale height is required in heating calculations for space vehicles re-entering the Earth's upper atmosphere. Density as well as chemical composition and temperature are needed in calculating a spacecraft's drag coefficient. Chemical composition and temperature also are required in the design of experiment sensors to be flown in this altitude range. Because of variability of atmospheric conditions with spatial location and solar condition, invariant models of the Earth's atmosphere (120 to 1000 kilometers) would not be useful for most engineering applications. Therefore, this monograph presents a computerized version of Jacchia's prediction method to provide models of the Earth's atmosphere which vary with solar condition and location. The resulting atmospheric models, which are predicted for particular times and locations, provide atmospheric density, chemical composition, temperature, molecular mass, and density scale height between 120 and 1000 kilometers altitude. In addition to the computerized method, a quick-look prediction method is given that may be used to obtain an estimate of atmospheric density for any time and spatial location without the use of a computer. A sample problem illustrates this method. Both methods provide models of mean density and models having reasonable upper extremes for density. The analytical approaches in both methods are considered to be the best available, but they could be refined considerably by additional data and study. Information contained in this monograph applies to altitudes between 120 and 1000 kilometers; other design criteria monographs in this series will provide atmospheric information below this altitude region.

Weidner, D. K.↗

Optimal rendezvous in the neighborhood of a circular orbit

The minimum velocity-change rendezvous solutions, when the motion may be linearized about a circular orbit, fall into two separate regions; the phase-for-free region and the general region. Phase-for-free solutions are derived from the optimum transfer solutions, require the same velocity-change expenditure, but may not be unique. Analytic solutions are presented in two of the three subregions. An algorithm is presented for determining the unique solutions in the general region. Various sources of initial conditions are discussed and three examples are presented.

Jones, J. B.↗

Typical motions in multiple systems

In very old times, people counted - one, two, many. The author wants to show that they were right. Consider the motions of isolated bodies: (1) N = 1 - simple motion; (2) N = 2 - Keplerian orbits; and (3) N = 3 - this is the difficult problem. In general, this problem can be studied only by computer simulations. The author studied this problem over many years (see, e.g., Agekian and Anosova, 1967; Anosova, 1986, 1989 a,b). The principal result is that two basic types of dynamics take place in triple systems. The first special type is the stable hierarchical systems with two almost Keplerian orbits. The second general type is the unstable triple systems with complicated motions of the bodies. By random choice of the initial conditions, by the Monte-Carlo method, the stable systems comprised about approx. 10% of the examined cases; the unstable systems comprised the other approx. 90% of cases under consideration. In N greater than 3, the studies of dynamics of such systems by computer simulations show that we have in general also the motions roughly as at the cases 1 - 3 with the relative negative or positive energies of the bodies. In the author's picture, the typical trajectories of the bodies in unstable triple systems of the general type of dynamics are seen. Such systems are disrupted always after close triple approaches of the bodies. These approaches play a role like the gravitational slingshot. Often, the velocities of escapers are very large. On the other hand, the movie also shows the dynamical processes of a formation, dynamical evolution and disruption of the temporary wide binaries in triples and a formation of final hard massive binaries in the final evolution of triples.

Anosova, Joanna P.↗

Dynamics of the Lunar Spin Axis

The evolution of the lunar spin axis is studied. Prior work has assumed that the inclination of the lunar orbit is constant and that the node regresses uniformly. This work takes into account the nonconstant inclination and nonuniform regression of the node as determined from averaged models of the motion of the lunar orbit. The resulting dynamics is considerably more rich, exhibiting additional resonances, period doubling and tripling, and chaos.

Wisdom, Jack↗

Computational methods and software systems for dynamics and control of large space structures

The deployment, assembly and mission-oriented maneuvering of space structures in orbit will trigger large motions of flexible, truss-type structures. In addition, the presence of on-board controls both for attitude stabilization and specified vibration tolerance requirements may further complicate the dynamic behavior of the orbiting structures. Because of safety and cost considerations, the dynamic response of the combined structural and control systems must be predicted reliably. This need can only be met through the development of reliable and efficient simulation capabilities, since there is general agreement that on-orbit experiments should be limited because of cost, time and facility constraints. The long-term objective of this research effort is to develop a next-generation computer simulator for the dynamics and control of large space structures. The simulator will be based on integrating four research thrusts: a new multibody dynamics formulation methodology, modeling capabilities in long/slender truss-beam components with realistic joints, efficient computational procedures that can be implemented either in sequential or concurrent computers, and prototype simulation modules that can be easily processed into a modern large-scale engineering software system such as the NASA/Computational Structural Mechanics (CSM) testbed.

Park, K. C.↗

Effects of atomic oxygen on graphite ablation

It is shown that a previously derived semiempirical equation for describing observed ablation rates of isotropic graphites cannot be applied to low-density flows containing dissociated oxygen. Experimentally determined reaction probabilities of isotropic graphites to molecular and atomic oxygen are used to calculate heat-transfer rates and stagnation-point ablation rates for typical conditions. Integrated mass losses are computed for a group of flight trajectories which start from geosynchronous orbit and enter earth's atmosphere in a skipping motion following near-elliptic decaying orbits. A comparison of the results with those obtained by the equation under question shows excellent agreement for steep trajectories, but large discrepancies for shallow trajectories. The differences are attributed to surface oxidation by atomic oxygen.

Park, C.↗

Particle orbits in a rotating liquid

The motion of small spherical particles under gravity, in a viscous fluid rotating uniformly about a horizontal axis, is investigated. Formulations and solutions are obtained for the particle orbit problem and the rotation rate optimization problem. It was found that the rotation rate which maximizes the fraction of the reactor cross-section area containing particles that will not spiral out to the wall in the experimental time (for heavy particles), or that have spiraled inward without hitting the wall (for light particles) is close to 1 rpm.

Roberts, Glyn O.↗