Relative motion of two particles in elliptic orbits
Two particles relative motion in elliptical orbits in inverse square central force field
Lancaster, E. R.↗
SEARCH · Engineering Papers
Results for “Relative Motion”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
A test of alternative Caribbean plate relative motion models
The new NUVEL-1 data set for global relative plate motions is used here to discriminate between the two prevailing models for Caribbean plate motion. One model, by Jordan (1975), assumes that North America-Caribbean motion is reflected by the spreading rate inferred from magnetic anomalies at the Cayman Spreading Center and the azimuths of nearby transforms. The other model, by Sykes et al. (1982), uses rates and azimuths inferred from the geometry of the Lesser Antilles Wadati-Benioff zone. Overall, it is found that the data fit the Jordan geometry better, that the data used in global plate motion models are more suitable than rates and azimuths inferred from the geometry of the Wadati-Benioff zone for determining relative motions, and that incorporation of all relevant plate boundaries is essential.
Stein, Seth↗
Relative motion of orbiting particles under the influence of perturbing forces. Volume 2: Analytical results
The mathematical developments carried out for this investigation are reported. In addition to describing and discussing the solutions which were acquired, there are compendia of data presented herein which summarize the equations and describe them as representative trace geometries. In this analysis the relative motion problems have been referred to two particular frames of reference; one which is inertially aligned, and one which is (local) horizon oriented. In addition to obtaining the classical initial values solutions, there are results which describe cases having applied specific forces serving as forcing functions. Also, in order to provide a complete state representation the speed components, as well as the displacements, have been described. These coordinates are traced on representative planes analogous to the displacement geometries. By this procedure a complete description of a relative motion is developed; and, as a consequence range rate as well as range information is obtained.
Eades, J. B., Jr.↗
Relative Motion of Two Spacecraft Near the Sun-Earth L2 Point
Over the next two decades international space agencies including the National Aeronautics and Space Administration and the European Space Agency are proposing space missions which employ distributed spacecraft technologies to enable vast improvements in remote sensing performance as compared to fundamental performance limitations associated with fairing sizes of even the largest launch vehicles. These missions will require numerous advanced technologies to enable some extreme scientific goals. However, on the critical path to developing many of those technologies, understanding realistic achievable performance, and formulating such missions involving formation flying spacecraft, is the detailed understanding of the vehicle relative motion in the appropriate dynamic environment. Due to the appealing gravitational and thermal environment, the Sun-Earth L(sub 2) point is a strong candidate for placement of many of these missions. Henceforth, this paper begins to unravel the dynamics of relative motion near L(sub 2), with particular consideration given to the ultimate requirements for flying space- craft in precise formation. This work is meant to be a predecessor to detailed formation flying mission analysis efforts in the areas of formation design, formation control, and relative navigation.
Collange, Guillaume↗
New Worlds Observer Formation Control Design Based on the Dynamics of Relative Motion
The New Worlds Observer (NWO) mission is designed for the direct detection and characterization of extrasolar planets. The NWO mission concept employs a two spacecraft leader-follower formation on a trajectory around the Earth/Moon-Sun L(sub 2) Libration Point. The leader spacecraft is baselined as a 4 meter optical telescope. The follower, Starshade spacecraft, is designed to suppress light from a central body star permitting direct detection of a surrounding exoplanetary system. The current design requires a nominal leader-follower separation range of 72 Megameters. NWO poses many challenges including formation control. NWO cycles between three principal control modes during the nominal mission timeline: science (fine pointing), realignment and transition. This paper examines formation control strategies in the context of dynamics of relative motion for two spacecraft operating in the vicinity of the Earth/Moon-Sun L(sub 2)libration point. The paper presents an overview of the equations of relative motion followed by a discussion of each of the control modes. Discussion and analysis characterize control strategies for each of the mission control modes, including requirements, implementation challenges and project fuel budgets.
Luquette, Richard J.↗
Generation of light by the relative motion of contiguous surfaces of mercury and glass.
Light generation by relative motion of mercury and helium contained in UV transmitting glass, noting intensity decrease with prolonged rotation
GLASS↗
A comparison of an analytical and numerical solution of the relative motion of two close satellites of an oblate planet
Comparison of analytical relative motion theory with numerical solution for equations of planar motion for two satellites of oblate planet
Barbier, R. W.↗
The relative motion of unrestrained bodies within orbiting space stations
Linearized perturbation theory for calculating relative motion of unrestrained bodies within orbiting space stations
Lee, W. N.↗
The primer vector in linear, relative-motion equations
Primer vector theory is used in analyzing a set of linear, relative-motion equations - the Clohessy-Wiltshire equations - to determine the criteria and necessary conditions for an optimal, N-impulse trajectory. Since the state vector for these equations is defined in terms of a linear system of ordinary differential equations, all fundamental relations defining the solution of the state and costate equations, and the necessary conditions for optimality, can be expressed in terms of elementary functions. The analysis develops the analytical criteria for improving a solution by (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of (1) fixed-end conditions, two-impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized rendezvous problem. A sequence of rendezvous problems is solved to illustrate the analysis and the computational procedure.
Source record↗
Relative motion of orbiting particles under the influence of perturbing forces. Volume 1: Summary
The relative motion for orbiting vehicles, under the influence of various perturbing forces, has been studied to determine what influence these inputs, and others, can have. The analytical tasks are discribed in general terms; the force types considered, are outlined modelled and simulated, and the capabilities of the computer programs which have evolved in support of this work are denoted.
Eades, J. B., Jr.↗
Primer vector theory applied to the linear relative-motion equations
Prime vector theory is used in analyzing a set of linear relative-motion equations - the Clohessy-Wiltshire (C/W) equations - to determine the criteria and necessary conditions for an optimal N-impulse trajectory. The analysis develops the analytical criteria for improving a solution by: (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of: (1) fixed-end conditions, two impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized renezvous problem.
Jezewski, D.↗
Unsteady aerodynamic simulation of multiple bodies in relative motion
A prototype method for time-accurate simulation of multiple aerodynamic bodies in relative motion is presented. The method is general and features unsteady chimera domain decomposition techniques and an implicit approximately factored finite-difference procedure to solve the time-dependent thin-layer Navier-Stokes equations. The method is applied to a set of two- and three-dimensional test problems to establish spatial and temporal accuracy, quantify computational efficiency, and begin to test overall code robustness.
Meakin, Robert L.↗
Tethered body problems and relative motion orbit determination
Selected problems dealing with orbiting tethered body systems have been studied. In addition, a relative motion orbit determination program was developed. Results from these tasks are described and discussed. The expected tethered body motions were examined, analytically, to ascertain what influence would be played by the physical parameters of the tether, the gravity gradient and orbit eccentricity. After separating the motion modes these influences were determined; and, subsequently, the effects of oscillations and/or rotations, on tether force, were described. A study was undertaken, by examining tether motions, to see what type of control actions would be needed to accurately place a mass particle at a prescribed position relative to a main vehicle. Other applications for tethers were studied. Principally these were concerned with the producing of low-level gee forces by means of stabilized tether configurations; and, the initiation of free transfer trajectories from tether supported vehicle relative positions.
Eades, J. B., Jr.↗
Three-dimensional unstructured method for flows past bodies in 6-DOF relative motion
A three dimensional, unstructured-mesh methodology was developed to simulate unsteady flows past bodies in relative motion, where the trajectory was determined from the instantaneous aerodynamics. The method coupled the equations of fluid flow and those of rigid-body dynamics, and captured the time-dependent interference between stationary and moving boundaries. The unsteady, compressible Euler equations were solved on dynamic, unstructured meshes by an explicit, finite-volume, upwind method. The grid adaptation was performed within a window placed around the moving body. The Euler equations of dynamics were solved by a Runge-Kutta integration scheme. The flow solver and the adaptation scheme were validated by simulating the transonic, unsteady flow around a wing undergoing a forced, periodic pitching motion, then comparing the results with the experimental data. To validate the trajectory code, the six-degrees-of-freedom (DOF) motion of a store separating from a wing was computed using the experimentally determined force and moment fields, then comparing with an independently generated trajectory. Finally, the overall methodology was demonstrated by simulating the unsteady flowfield and the trajectory of a store dropped from a wing. The methodology, its computational cost notwithstanding, has proven to be accurate, automated, easy for dynamic gridding, and relatively efficient for the required man-hours.
Singh, K. P.↗
Unsteady aerodynamic simulation of multiple bodies in relative motion: A prototype method
A prototype method for time-accurate simulation of multiple aerodynamic bodies in relative motion is presented. The method is general and features unsteady chimera domain decomposition techniques and an implicit approximately factored finite-difference procedure to solve the time-dependent thin-layer Navier-Stokes equations. The method is applied to a set of two- and three- dimensional test problems to establish spatial and temporal accuracy, quantify computational efficiency, and begin to test overall code robustness.
Meakin, Robert L.↗
Relative motions of fragments of the split comets. I - A new approach
A hypothesis is proposed which interprets the relative motion of two fragments of a split comet in terms of a slight difference between their effective solar attraction rather than in terms of the impulse imparted to them at separation. A quantitative version of this hypothesis is formulated by assuming that the difference in effective solar attraction varies with heliocentric distance in direct proportion to the actual solar attraction so that the ratio of the two forces is constant and equal to a measure of the relative effect between the two fragments under consideration. Results obtained using this formulation are compared with observational evidence on the split comets P/Biela, Liais 1860 I, 1882 II, P/Brooks 2 1889 V, Swift 1899 I, Kopff 1905 IV, Mellish 1915 II, Taylor 1916 I, 1947 XII, Wirtanen 1957 VI, Ikeya-Seki 1965 VIII, Kohoutek 1970 III, and West 1975n. The hypothesis is found to fail only in the case of comet Wirtanen 1957 VI. Some unusual phenomena associated with split comets are examined.
Sekanina, Z.↗
Control of the relative motion between satellites in neighboring elliptic orbits
Relative translational motion control, and motion stability between satellites in neighboring elliptical orbits
TRANSLATIONAL MOTION↗
Preliminary determination of Pacific-North America relative motion in the southern Gulf of California using the Global Positioning System
GPS data from experiments conducted in 1985 and 1989 in the southern Gulf of California, Mexico, allow a determination of relative motion between the Pacific and North American plates. The data indicate motion by Cabo San Lucas on the Pacific plate relative to North America at a rate of 47 + or - 7 mm/yr and azimuth of 57 + or - 6 deg west of north, equivalent within uncertainties to the NUVEL-1 global plate motion model.
Dixon, T. H.↗