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Results for “MOTION EQUATION”

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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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Optimal trajectories for the Aeroassisted Flight Experiment. Part 1: Equations of motion in an Earth-fixed system

The determination of optimal trajectories for the aeroassisted flight experiment (AFE) is discussed. The AFE refers to the study of the free flight of an autonomous spacecraft, shuttle-launched and shuttle-recovered. Its purpose is to gather atmospheric entry environmental data for use in designing aeroassisted orbital transfer vehicles (AOTV). It is assumed that: (1) the spacecraft is a particle of constant mass; (2) the Earth is rotating with constant angular velocity; (3) the Earth is an oblate planet, and the gravitational potential depends on both the radial distance and the latitude (harmonics of order higher than four are ignored); and (4) the atmosphere is at rest with respect to the Earth. Under these assumptions, the equations of motion for hypervelocity atmospheric flight (which can be used not only for AFE problems, but also for AOT problems and space shuttle problems) are derived in an Earth-fixed system. Transformation relations are supplied which allow one to pass from quantities computed in an Earth-fixed system to quantities computed in an inertial system, and vice versa.

Miele, A.↗
NASA NTRS1980

Generic multi-body formulation of heavy lift airship equations of motion

This paper describes the formulation of a comprehensive set of equations which describe the dynamic behavior of a generic heavy lift airship (HLA). They are being used in a digital computer simulation to investigate the response dynamics and flying qualities of HLAs operating with various payloads in a variety of operational environments. A key feature is the separate treatment of each component body making up the HLA. This allows the analyst to vary the configuration (e.g., number of lift-propulsion units, presence or absence of slung payload, etc.) without rewriting the equations. It further provides measures of key structural and control loads acting on the HLA and eases the task of modeling wind disturbances.

Ringland, R. F.↗
NASA NTRS1982

Nonlinear equations of motion for Landau resonance interactions with a whistler mode wave

A simple set of equations is presented for the description of the cyclotron averaged motion of Landau resonant particles in a whistler mode wave propagating at an angle to the static magnetic field. A comparison is conducted of the wave magnetic field and electric field effects for the parameters of the magnetosphere, and the parameter ranges for which the wave magnetic field effects would be negligible are determined. It is shown that the effect of the wave magnetic field can be neglected for low pitch angles, high normal wave angles, and/or high normalized wave frequencies.

Inan, U. S.↗
NASA NTRS1971

On the integrability cases of the equation of motion for a satellite in an axially symmetric gravitational field.

Investigation of two cases of integrability of a second-order differential equation describing the projection of an axisymmetric satellite orbit on to a plane perpendicular to the rotation axis. It is demonstrated that for these two cases the integration can be carried out either by quadratures or reduced to a first-order differential equation. Analytical and physical properties are expressed, and it is shown that the equation can be derived from the classical plane eikonal equation of geometric optics.

Ghaffari, A.↗
NASA NTRS2005

Perturbed Equations of Motion for Formation Flight Near the Sun-Earth L2 Point

NASA is planning missions to the vicinity of the Sun-Earth L(sub 2) point, some involving a distributed system of telescope spacecraft, configured in a plane about a hub. Several sets of differential equations are written for the formation flight of such telescopes relative to the hub, with varying levels of fidelity. Effects are cast as additive perturbations to the circular restricted three-body problem, expanded in terms of the system distanced, to an accuracy of 10-20 m. These include Earth's orbital eccentricity, lunar motion, solar radiation pressure, and small thrusting forces. Simulations validating the expanded differential equations are presented.

Luquette, Richard↗
NASA NTRS1980

Collisional redistribution of radiation. III - The equation of motion for the correlation function and the scattered spectrum

Computations were made of the scattering of monochromatic radiation by a degenerate atom in the binary-collision approximation for field strengths whose products of the Rabi frequency for atomic transition and the duration of a strong collision are much less than 1. An expression of motion for the correlation function is derived which does not exclude the region where thermal correlations may be neglected; the equation is valid outside the quantum-regression regime, and has a straightforward solution for practical cases. Solutions for the weak-field linear response regime are presented in terms of generalized absorption and emission profiles which depend on the indices of the atomic multipoles.

Burnett, K.↗
NASA NTRS1972

Equations of motion in the linear approximation.

Attempt to develop a gauge-invariant theory of the motion of singularities in an n-dimensional Riemannian space. A gauge-invariant theory is developed for a nongeodetic particle represented by a time-like world line in the linearized field theory. The solution of the basic algebraic and differential equations is to be constructed from the source line, the future null cones emanating from it, a scale factor, and nothing else, and the leading term of the solution is the Schwarzschild field. A class of possible solutions is examined, and it is shown that this class contains just one acceptable member - namely, a particle in constant acceleration.

Robinson, I.↗
NASA NTRS2001

Multi-Tethered Space-Based Interferometers: Particle System Model

Dynamics models are presented for a class of space-based interferometers comprised of multiple component bodies, interconnected in various arrangements, by low-mass flexible tethers of variable length. The tethered constellations are to perform coordinated rotational scanning accompanied by baseline dimensional changes, as well as spin axis realignments and spin-up/spin-down maneuvers. The mechanical idealization is a system of N point masses interconnected by massless tethers of variable length. Both extensible and inextensible tethers are considered. Expressions for system angular and linear momenta are developed. The unrestricted nonlinear motion equations are derived via Lagranges equations. Rheonomic constraints are introduced to allow prescribed motion of any degrees of freedom, and the associated physical forces are determined. The linearized equations of motion are obtained for the steady rotation of a system with extensible tethers of constant unstrained length.

Gates, Stephen S.↗