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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Relative motion of orbiting particles under the influence of perturbing forces. Volume 3: Construction of relative motion traces

Geometric traces can be simply constructed to illustrate the relative motions experienced by particles in a number of problem situations. These diagrams describe the displacements and hodographs which arise as a consequence of initial value inputs and selected disturbance (force) conditions. Due to the linearization which is imposed on the mathematical formulation there is a separation of the in-plane and out-of-plane coordinate solutions. The construction of in-plane traces is easier to represent and to visualize. The out-of-plane geometries are the more complicated cases and generally need some added specializations in order to acquire figures which have some degree of symmetry and simplicity.

Eades, J. B., Jr.↗
NASA NTRS1972

Relative motion of orbiting satellites

The relative motion problem is analyzed, as a linearized case, and as a numerically determined solution to provide a time history of the geometries representing the motion state. The displacement history and the hodographs for families of solutions are provided, analytically and graphically, to serve as an aid to understanding this problem area. Linearized solutions to relative motion problems of orbiting particles are presented for the impulsive and fixed thrust cases. Second order solutions are described to enhance the accuracy of prediction. A method was developed to obtain accurate, numerical solutions to the intercept and rendezvous problem; and, special situations are examined. A particular problem related to relative motions, where the motion traces develop a cusp, is examined in detail. This phenomenon is found to be dependent on a particular relationship between orbital eccentricity and the inclination between orbital planes. These conditions are determined, and, example situations are presented and discussed.

Eades, J. B., Jr.↗
NASA NTRS2004

Linear State-Space Representation of the Dynamics of Relative Motion, Based on Restricted Three Body Dynamics

Precision Formation Flying is an enabling technology for a variety of proposed space- based observatories, including the Micro-Arcsecond X-ray Imaging Mission (MAXIM), Stellar Imager (SI) and the Terrestrial Planet Finder (TPF). An essential element of the technology is the control algorithm, requiring a clear understanding of the dynamics of relative motion. This paper examines the dynamics of relative motion in the context of the Restricted Three Body Problem (RTBP). The natural dynamics of relative motion are presented in their full nonlinear form. Motivated by the desire to apply linear control methods, the dynamics equations are linearized and presented in state-space form. The stability properties are explored for regions in proximity to each of the libration points in the Earth/Moon - Sun rotating frame. The dynamics of relative motion are presented in both the inertial and rotating coordinate frames.

Luquette, Richard J.↗
NASA NTRS2004

Linear State-Space Representation of the Dynamics of Relative Motion, Based on Restricted Three Body Dynamics

Precision Formation Flying is an enabling technology for a variety of proposed space-based observatories, including the Micro-Arcsecond X-ray Imaging Mission (MAXIM) , the associated MAXIM pathfinder mission, Stellar Imager (SI) and the Terrestrial Planet Finder (TPF). An essential element of the technology is the control algorithm, requiring a clear understanding of the dynamics of relative motion. This paper examines the dynamics of relative motion in the context of the Restricted Three Body Problem (RTBP). The natural dynamics of relative motion are presented in their full nonlinear form. Motivated by the desire to apply linear control methods, the dynamics equations are linearized and presented in state-space form. The stability properties are explored for regions in proximity to each of the libration points in the Earth/Moon - Sun rotating frame. The dynamics of relative motion are presented in both the inertial and rotating coordinate frames.

Luquette,Richard J.↗
NASA NTRS1973

Relative motion of near orbiting satellites.

The relative motion of two particles on adjacent orbits about the same primary has been investigated under the condition that both motions have the same period. The geometrical properties of the relative displacement and velocity traces, on representative planes, are studied. A complete state of the motion is given; and, the range and range-rate variations, over one or more orbits, are described. It has been found that cusps appear on some of the traces provided that a proper relationship exists between the eccentricity and inclination. (Here, one particle moves on a circular path while the second moves on an ellipse). The conditions for which cusps appear are given, and typical traces are shown.

Eades, J. B., Jr.↗
NASA NTRS2004

Relative-Motion Sensors and Actuators for Two Optical Tables

Optoelectronic sensors and magnetic actuators have been developed as parts of a system for controlling the relative position and attitude of two massive optical tables that float on separate standard air suspensions that attenuate ground vibrations. In the specific application for which these sensors and actuators were developed, one of the optical tables holds an optical system that mimics distant stars, while the other optical table holds a test article that simulates a spaceborne stellar interferometer that would be used to observe the stars. The control system is designed to suppress relative motion of the tables or, on demand, to impose controlled relative motion between the tables. The control system includes a sensor system that detects relative motion of the tables in six independent degrees of freedom and a drive system that can apply force to the star-simulator table in the six degrees of freedom. The sensor system includes (1) a set of laser heterodyne gauges and (2) a set of four diode lasers on the star-simulator table, each aimed at one of four quadrant photodiodes at nominal corresponding positions on the test-article table. The heterodyne gauges are used to measure relative displacements along the x axis.

Gursel, Yekta↗
NASA NTRS2025

Robust Trajectory Optimization for NRHO Rendezvous Using SPICE Kernel Relative Motion

In this paper, robust optimization is performed on trajectory correction maneuvers during the lunar lander return phase of an Artemis mission, treating the trajectory from one hour after low lunar orbit departure to arrival in the vicinity of the lunar Gateway as a relative motion problem. To enable rapid stochastic optimization techniques requiring many candidate trajectories, SPICE kernel relative motion as implemented by the Quadratic Interpolated State Transition (QIST) system is used as the underlying dynamics propagation. The optimization is performed with a genetic optimizer using linear covariance (LinCov) software in a simplified operational context, taking into account the availability of navigation sensors with varying measurement models, ranges, and accuracies. No numerical integration is used, since the relative motion around Gateway is fully characterized with the a priori computation of the QIST coefficients. Maneuver placements are computed to optimize the minimum 3σ delta-v of the trajectory, the position dispersion at a target point, and a convex combination of these two metrics. An order of magnitude runtime improvement is provided over legacy methods with less than 10% error introduced. All QIST results are shown to be in-family with legacy methods. The tradespace for optimal delta-v design is found to range from 77.0 to 93.9 m/s, while the range of optimal dispersion is between 1.4 and 11.7 km.

Relative Motion↗
NASA NTRS1991

Use of non-spherical gravity harmonics for relative motion GN/C (category 2)

Detailed analysis of the Automatic Rendezvous and Capture problem indicate a need for three different regions of mathematical description for the GN&C algorithms: (1) multi-vehicle orbital mechanics to the rendezvous interface point, i.e., within 100 nm; (2) relative motion solutions (such as Clohessy-Wiltshire type) from the far-field to the near-field interface, i.e., within 1 nm and; (3) close proximity motion - the near-field motion where the relative differences in the gravitational and orbit inertial accelerations can be neglected from the equations of motion. Limit boundaries to these regions can be precisely defined by further analysis and will be functions of the tracking measurement accuracies and the computer resources available for the solution of the algorithms. This paper analyzes the relative motion in Regions 2 and 3 above and present the derivation and discussion of the general case of non-spherical gravitational perturbed relative motion. Mathematical deviations from the numerically integrated spherical gravity case and solutions from the Clohessy-Wiltshire equations are presented in the analysis. Based upon this preliminary analysis, it is recommended that further efforts be used to assess the relative position and velocity differences in Region 2 due to non-spherical gravity harmonics and that viable GN&C algorithms be developed to include these gravity perturbations (especially the effects of the first gravity harmonic, J2).

Henderson, David M.↗
NASA NTRS2004

Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion

Geometrical methods for formation flying design based on the analytical solution to Hill's equations have been previously developed and used to specify desired relative motions in near circular orbits. By generating relationships between the vehicles that are intuitive, these approaches offer valuable insight into the relative motion and allow for the rapid design of satellite configurations to achieve mission specific requirements, such as vehicle separation at perigee or apogee, minimum separation, or a specific geometrical shape. Furthermore, the results obtained using geometrical approaches can be used to better constrain numerical optimization methods; allowing those methods to converge to optimal satellite configurations faster. This paper presents a set of geometrical relationships for formations in eccentric orbits, where Hill.s equations are not valid, and shows how these relationships can be used to investigate formation designs and how they evolve with time.

Lane, Christopher↗
NASA NTRS1984

Relative motion characteristics of 2 near-Earth Satellites

The stability of the nonlinear dynamical system of two GRAVSAT - type satellites was investigated by performing several numerical experiments which provide the simulations of the relative motion characteristics between the two satellites for various specified time intervals. The simulations included the relative range, range-rate, and relative acceleration magnitude. These simulations were generated with respect to appropriate initial orbital elements which were obtained such that the instantaneous separation distance between the two satellites has small fluctuations from a specified constant separation distance. The simulation results indicate that the behavior of the relative motions is very sensitive to the initial orbital elements of the satellites and that for a specified time interval of interest. A stable behavior is possible only with the use of an appropriate set of initial orbital elements compatible with the gravity field used to derive them.

Schutz, B. E.↗
NASA NTRS1976

The computation of relative motion with increased precision

Encke's method as modified by Potter to increase the accuracy of orbit computations of gravitationally interacting bodies is applied to the problem of relative motion of non-interacting space vehicles. This technique is then combined with a simple transformation of the independent variable to arrive at a system of equations from which the relative motion may be determined with increased precision.

Nacozy, P.↗