Three-dimensional nonlinear stability analysis of the sun-perturbed earth-moon equilateral points.
Nonlinear analysis of earth-moon system motion stability in three dimensions near L4 libration point when perturbed by sun
PERTURBATION THEORY↗
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Solution of the exact equations for three-dimensional atmospheric entry using directly matched asymptotic expansions
The problem of determining the trajectories, partially or wholly contained in the atmosphere of a spherical, nonrotating planet, is considered. The exact equations of motion for three-dimensional, aerodynamically affected flight are derived. Modified Chapman variables are introduced and the equations are transformed into a set suitable for analytic integration using asymptotic expansions. The trajectory is solved in two regions: the outer region, where the force may be considered a gravitational field with aerodynamic perturbations, and the inner region, where the force is predominantly aerodynamic, with gravity as a perturbation. The two solutions are matched directly. A composite solution, valid everywhere, is constructed by additive composition. This approach of directly matched asymptotic expansions applied to the exact equations of motion couched in terms of modified Chapman variables yields an analytical solution which should prove to be a powerful tool for aerodynamic orbit calculations.
Busemann, A.↗
The dynamics and control of large flexible space structures. Volume 3, part B: The modelling, dynamics, and stability of large Earth pointing orbiting structures
The dynamics and stability of large orbiting flexible beams, and platforms and dish type structures oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid light-weight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam, the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate and shallow spherical shell in orbit with a two-degree-of freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for all the examples and a sensitivity study of the system response characteristics to the key system parameters is carried out.
Bainum, P. M.↗
On the dynamics of large orbiting flexible beams and platforms oriented along the local horizontal
The dynamics and stability of large orbiting flexible beams and platforms oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid lightweight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam it is seen that the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate in orbit with a two-degree-of-freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for both examples and a parametric study of the least damped mode characteristics together with numerically simulated transient responses are carried out.
Bainum, P. M.↗
Analysis of Particle Motions for a Class of Three-dimensional Incompressible Laminar Boundary Layers
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Hansen, Arthur G↗
The effect of 3-dimensional nonlinear resonances on the motion of a particle near the earth-moon equilateral libration points
Three dimensional resonance effects on particle motion stability near earth-moon equilateral libration points
Schechter, H. B.↗
Analytic construction of periodic orbits about the collinear points
A third-order analytical solution for halo-type periodic motion about the collinear points of the circular-restricted problem is presented. The three-dimensional equations of motion are obtained by a Lagrangian formulation. The solution is constructed using the method of successive approximations in conjunction with a technique similar to the Lindstedt-Poincare method. The theory is applied to the sun-earth system.
Richardson, D. L.↗
A derivation of the three dimensional three degree of freedom re-entry equations of motion in terrestrial navigational coordinates with subsequent resolution into inertial platform coordinates
Derivation of three-dimensional three-degree-of- freedom reentry equations of motion in terrestrial navigational coordinates
REENTRY GUIDANCE↗
Time-dependent calculation of a forced mixing layer using a k-epsilon turbulence model
A two-dimensional-dependent calculation of a forced turbulent mixing layer is reported. The approach employs a k-epsilon turbulence model to represent the effects of motions which are three dimensional or out of phase with the forcing cycle. Calculations that correspond to conditions of the measurements of Weisbrot (1984) and Weisbrot and Wygnanski (1988) indicate that the main features of the mixing layer development are captured by the computation. The effect of grid refinement on the computed result indicates the importance of adequate resolution of the near field in correctly reproducing the flow evolution. The inlet boundary condition, similarly, is shown to play a decisive role in determining subsequent development.
Macinnes, J. M.↗
Three-Dimensional Robotic Vision System
Stereoscopy and motion provide clues to outlines of objects. Digital image-processing system acts as "intelligent" automatic machine-vision system by processing views from stereoscopic television cameras into three-dimensional coordinates of moving object in view. Epipolar-line technique used to find corresponding points in stereoscopic views. Robotic vision system analyzes views from two television cameras to detect rigid three-dimensional objects and reconstruct numerically in terms of coordinates of corner points. Stereoscopy and effects of motion on two images complement each other in providing image-analyzing subsystem with clues to natures and locations of principal features.
Nguyen, Thinh V.↗
Particle motion in atmospheric boundary layers of Mars and Earth
To study the eolian mechanics of saltating particles, both an experimental investigation of the flow field around a model crater in an atmospheric boundary layer wind tunnel and numerical solutions of the two- and three-dimensional equations of motion of a single particle under the influence of a turbulent boundary layer were conducted. Two-dimensional particle motion was calculated for flow near the surfaces of both Earth and Mars. For the case of Earth both a turbulent boundary layer with a viscous sublayer and one without were calculated. For the case of Mars it was only necessary to calculate turbulent boundary layer flow with a laminar sublayer because of the low values of friction Reynolds number; however, it was necessary to include the effects of slip flow on a particle caused by the rarefied Martian atmosphere. In the equations of motion the lift force functions were developed to act on a single particle only in the laminar sublayer or a corresponding small region of high shear near the surface for a fully turbulent boundary layer. The lift force functions were developed from the analytical work by Saffman concerning the lift force acting on a particle in simple shear flow.
White, B. R.↗
Three-dimensional interplanetary stream magnetism and energetic particle motion
Cosmic rays interact with mesoscale configurations of the interplanetary magnetic field. A technique is presented for calculating such configurations in the inner solar system, which are due to streams and source conditions near the sun, and maps of magnetic field are constructed for some plausible stream and source conditions. One effect of these mesoscale configurations on galactic cosmic rays is shown to be an out-of-the-ecliptic gradient drift sufficient to explain Forbush decreases. The effects on solar energetic particles include small polar drifts due to the field gradients and a possibly large modification of the time-intensity profiles and anisotropy characteristics due to the formation of mirror configurations in space. If a diffusion model is applicable to solar particles, the true diffusion coefficient will be masked by the effects of streams. A conceptual model which incorporates these ideas and those of several other models is presented.
Barouch, E.↗
Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains
We use a combination of analytical and numerical methods to investigate the dynamics of charged dust grains in planetary magnetospheres. Our emphasis is on obtaining results valid for particles that are not necessarily dominated either by gravitational or electromagnetic forces. A Hamiltonian formulation of the problem yields exact results, for all values of charge-to-mass ratio, when we introduce two constraints: particles remain in the equatorial plane and the magnetic field is taken as axially symmetric. In particular, we obtain locations of equilibrium points, the frequencies of stable periodic orbits, the topology of separatrices in phase space, and the rate of longitudinal drift. These results are significant for specific applications: motion in the nearly aligned dipolar field of Saturn, and the trajectories of arbitrarily charged particles in complex magnetic fields for limited periods of time after ejection from parent bodies. Since the model is restrictive, we also use numerical integrations of the full three-dimensional equations of motion and illustrate under what conditions the constrained problem yields reasonable results. We show that a large fraction of the intermediately charged and highly charged (gyrating) particles will always be lost to a planet's atmosphere within a few hundred hours, for motion through tilted-dipole magnetic fields. We find that grains must have a very high charge-to-mass ratio in order to be mirrored back to the ring plane. Thus, except perhaps at Saturn where the dipole tilt is very small, the likely inhabitants of the dusty ring systems are those particles that are either nearly Keplerian (weakly charged) grains or grains whose charges place them in the lower end of the intermediate charge zone. Fianlly, we demonstrate the effect of plasma drag on the orbits of gyrating particles to be a rapid decrease in gyroradius followed by a slow radial evolution of the guiding center.
Schaffer, L.↗
Three-dimensional organization of vestibular related eye movements to rotational motion in pigeons
During rotational motions, compensatory eye movement adjustments must continually occur in order to maintain objects of visual interest as stable images on the retina. In the present study, the three-dimensional organization of the vestibulo-ocular reflex in pigeons was quantitatively examined. Rotations about different head axes produced horizontal, vertical, and torsional eye movements, whose component magnitude was dependent upon the cosine of the stimulus axis relative to the animal's visual axis. Thus, the three-dimensional organization of the VOR in pigeons appears to be compensatory for any direction of head rotation. Frequency responses of the horizontal, vertical, and torsional slow phase components exhibited high pass filter properties with dominant time constants of approximately 3 s.
NASA Discipline Neuroscience↗
The response of a constant-volume balloon to periodic three-dimensional flow
A theoretical treatment is presented of the motion of a constant-volume balloon immersed in a three-dimensional spatially nonhomogeneous periodic flow field with a mean translational flow velocity. The governing equations are the equations of conservation of momentum of the balloon, coupled with the equations of conservation of momentum of the fluid. In the mathematical model employed, the flow field is represented by a periodic function. The numerical results are in general agreement with observations. Noteworthy is that the balloon does not move with the same mean velocity as the wind and, thus, when Taylor's hypothesis for the fluid is satisfied, the balloon does not 'lock in' with the wind velocity. When Taylor's hypothesis for the parcel is satisfied, however, the balloon does match the mean wind direction (but not its speed).
Tatom, F. B.↗
Attitude stability of a gravity-stabilized gyrostat satellite
Gravity stabilized gyrostat satellite attitude motion stability, using three dimensional diagram and Liapunov functions
Crespo Da Silva, M. R. M.↗
Vibration of Shells
The vibrational characteristics and mechanical properties of shell structures are discussed. The subjects presented are: (1) fundamental equations of thin shell theory, (2) characteristics of thin circular cylindrical shells, (3) complicating effects in circular cylindrical shells, (4) noncircular cylindrical shell properties, (5) characteristics of spherical shells, and (6) solution of three-dimensional equations of motion for cylinders.
Leissa, A. W.↗
Ion kinematics in a plasma focus.
The results of numerical integrations of three-dimensional equations of motion of ions subject to given electric and magnetic fields are presented. The fields represent those which may exist in the pinch phase of the plasma focus, although here they depend only on the radial coordinate. The ions initially have Maxwellian velocity distributions, and their trajectories are interpreted in terms of single-particle constants of the motion. Two models of the axial electric field Ez are considered. For strong Ez away from the axis, there is a cyclotron acceleration which leads to ion heating. For positive Ez on the axis, ions within a Larmor radius of the axis undergo very efficient acceleration; the results for this new model are in general agreement with experimental results.
Gary, S. P.↗