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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

Boson Star from Repulsive Light Scalars and Gravitational Waves

We study properties of boson stars consisting of ultra-light scalar dark matter with repulsive self-interactions. We investigate the origin of the maximum mass of spherically symmetric stable stars which emerges only when solving the full equations of motion in curved space-time, but not when solving the approximated Schrödinger-Newton equations. When the repulsion is weak, the backreaction of the curvature on the scalars acts as an additional source of attraction and can overcome the repulsion, resulting in a maximum star mass and compactness. We also point out that the potential in a UV completed particle physics model of light scalar dark matter is generally more complicated than the widely used φ 4 interaction. Additional interactions beyond φ 4 in the potential can dramatically change the properties of boson stars as well as modify the prospect of LIGO gravitational wave detection for binary mergers of boson stars.

Djuna Croon↗
NASA NTRS1962

Analytical Study of the Tumbling Motions of Vehicles Entering Planetary Atmospheres

The tumbling motion of vehicles entering planetary atmospheres is analyzed. A differential equation governing the tumbling motion, its arrest, and the subsequent oscillatory motion is obtained and identified as the equation for the fifth Painleve transcendant. An approximate analytical solution for the transcendant is derived. Comparisons with results obtained from numerical integration of the exact equations of motion indicate that the solution for the angle-of-attack history is sufficiently accurate to be of practical use.

PLANETARY ENTRY↗
DOE OSTI2021

Kinklike structures in an arcsin real scalar dynamics

Highlights: • Kinklike analyses in a real scalar theory with an arcsin dynamic. • First-order formalism implementation and deformation procedure in an arcsin scalar dynamics. In this paper, we analyze kink-like analytical solutions in a real scalar theory with an arcsin dynamics inspired by the arcsin electrodynamics presented in Kruglov (2015). This analysis is done by means of the first-order formalism. This formalism provides a framework where the equations of motion can be simplified by preserving the linear stability of the theory. In this work, the deformation procedure is implemented with the aim of finding exact solutions in systems with generalized dynamics. Along the paper, we explore how the first-order formalism is implemented in the arcsin kinetics and how such a term influences the kink-like solutions. As a part of the result of our paper, we show that the kink-like solutions are similar to the ones obtained in the standard scalar kinetic theory. We also show that the extra parameter, that controls the non-linearities of the model, plays an essential role in the energy densities and stability potentials. These quantities vary according to this parameter. The goals here are to show how the first-order framework is implemented in this arcsin scenario and to present the analytical kink-like solutions that can be found by means of the first-order framework and deformation method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1955

Determination of lateral-stability derivatives and transfer-function coefficients from frequency-response data for lateral motions

A method is presented for determining the lateral-stability derivatives, transfer-function coefficients, and the modes for lateral motion from frequency-response data for a rigid aircraft. The method is based on the application of the vector technique to the equations of lateral motion, so that the three equations of lateral motion can be separated into six equations. The method of least squares is then applied to the data for each of these equations to yield the coefficients of the equations of lateral motion from which the lateral-stability derivatives and lateral transfer-function coefficients are computed. Two numerical examples are given to demonstrate the use of the method.

Donegan, James J↗
NASA NTRS1973

Applications of the Kustaanheimo-Stieffel transformation of the perturbed two-body problem

The Newtonian differential equations of motion for the two-body problem can be transformed into four linear harmonic-oscillator equations by simultaneously applying the regularization step dt/ds = r and the Kustaanheimo-Stieffel (KS) transformation. The regularization step changes the independent variable from time to a new variable s, and the KS transformation transforms the position and velocity vectors from Cartesian space into a four-dimensional space. A derivation of a uniform, regular solution for the perturbed two-body problem in the four-dimensional space is presented. The variation-of-parameters technique is used to develop expressions for the derivatives of ten elements (which are constants in the unperturbed motion) for the general case that includes both perturbations which can arise from a potential and perturbations which cannot be derived from a potential. This ten-element solution has mixed secular terms that degrade the long-term accuracy during numerical integration. Therefore, to eliminate these terms, the solution is modified by introducing two additional elements.

Bond, V. R.↗
NASA NTRS1990

Conical Euler solution for a highly-swept delta wing undergoing wing-rock motion

Modifications to an unsteady conical Euler code for the free-to-roll analysis of highly-swept delta wings are described. The modifications involve the addition of the rolling rigid-body equation of motion for its simultaneous time-integration with the governing flow equations. The flow solver utilized in the Euler code includes a multistage Runge-Kutta time-stepping scheme which uses a finite-volume spatial discretization on an unstructured mesh made up of triangles. Steady and unsteady results are presented for a 75 deg swept delta wing at a freestream Mach number of 1.2 and an angle of attack of 30 deg. The unsteady results consist of forced harmonic and free-to-roll calculations. The free-to-roll case exhibits a wing rock response produced by unsteady aerodynamics consistent with the aerodynamics of the forced harmonic results. Similarities are shown with a wing-rock time history from a low-speed wind tunnel test.

Lee, Elizabeth M.↗
DOE OSTI2024

On the Statistical Mechanics of Mass Accommodation at Liquid–Vapor Interfaces

Here we propose a framework for describing the dynamics associated with the adsorption of small molecules to liquid-vapor interfaces using an intermediate resolution between traditional continuum theories that are bereft of molecular detail and molecular dynamics simulations that are replete with them. In particular, we develop an effective single particle equation of motion capable of describing the physical processes that determine thermal and mass accommodation probabilities. The effective equation is parametrized with quantities that vary through space away from the liquid-vapor interface. Of particular importance in describing the early time dynamics is the spatially dependent friction, for which we propose a numerical scheme to evaluate from molecular simulation. Taken together with potentials of mean force computable with importance sampling methods, we illustrate how to compute the mass accommodation coefficient and residence time distribution. Throughout, we highlight the case of ozone adsorption in aqueous solutions and its dependence on electrolyte composition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1971

Aperiodic behaviour of a non-linear oscillator.

The aperiodic behavior of the solution of the equation of motion derived previously (1966) when considering a model thermomechanical oscillator is examined. Periodic solutions of this equation are studied numerically and analytically. Conditions for the instability of the solutions are determined. This instability seems to be the cause of the observed aperiodicity.

Baker, N. H.↗
NASA NTRS1972

Attitude control of a spinning Skylab.

Active attitude control of a spinning Skylab is analyzed to determine a simple control law that will provide a satisfactory response, considering the dynamics of attached flexible appendages. A simplified model of the complex Skylab vehicle is selected to make it analytically tractable. The vehicle is modeled as a single rigid-core body with two attached flexible massless booms having masses on their tips. The equations of motion describing the attitude dynamics of the model are presented as a linear matrix-differential equation. The states of the vehicle are small perturbations about its steady-state spin. An analysis is performed to determine the domain of stability. Next, attitude dynamics are analyzed; both frequency domain (parameter plane) and time domain (an optimal linear quadratic loss program) techniques are compared. An analysis of the nonlinear effect of control torque saturation of Skylab's control moment gyroscopes is discussed. The results of the analysis compare favorably with a large-scale digital simulation of the Skylab.

Seltzer, S. M.↗
NASA NTRS1975

Time elements

Time elements are introduced for use with Sundman time transformations for satellite equations of motion. Two time elements are presented, one providing maximum accuracy when the exponent of the governing equation equals 1, the other when the exponent equals 2. Time elements and time transformations reduce local truncation error and Liapunov (in-track) instability, and provide analytical step size control. Numerical results show accuracy improvements of more than one order of magnitude when time elements are employed with time transformations in the numerical integration of the satellite equations, compared with using time transformations alone.

Nacozy, P. E.↗
NASA NTRS1976

A mathematical simulation model of a 1985-era tilt-rotor passenger aircraft

A mathematical model for use in real-time piloted simulation of a 1985-era tilt rotor passenger aircraft is presented. The model comprises the basic six degrees-of-freedom equations of motion, and a large angle of attack representation of the airframe and rotor aerodynamics, together with equations and functions used to model turbine engine performance, aircraft control system and stability augmentation system. A complete derivation of the primary equations is given together with a description of the modeling techniques used. Data for the model is included in an appendix.

Mcveigh, M. A.↗
NASA NTRS1979

Influence of a weak gravitational wave on a bound system of two point-masses

The problem of a weak gravitational wave impinging upon a nonrelativistic bound system of two point masses is considered. The geodesic equation for each mass is expanded in terms of two small parameters, v/c and dimensionless wave amplitude, in a manner similar to the post-Newtonian expansion; the geodesic equations are resolved into orbital and center-of-mass equations of motion. The effect of the wave on the orbit is determined by using Lagrange's planetary equations to calculate the time evolution of the orbital elements. The gauge properties of the solutions and, in particular, the gauge invariance of the secular effects are discussed.

Turner, M. S.↗
NASA NTRS1981

On numerical nonlinear analysis of highly flexible spinning cantilevers

The general nonlinear discretized equations of motion of spinning elastic solids and structures are derived as a set of nonlinear ordinary differential equations for the case when the strain-displacement and velocity-displacement relations are nonlinear up to the second order. It is shown that the cost of generation of such equations is proportional to the fourth power of the number of degrees of freedom. A computer program is written to automatically generate the equations for the case of spinning cantilevers with initial imperfections. The types and the number of the coordinate functions used in the trial solution are parameters of the program.

Utku, S.↗
NASA NTRS1985

Orbital Resonances and Planetary Accretion in the Solar Nebula

Planetesimal orbital evolution in a resisting medium near an accreting protoplanet was studied to explore mechanisms for capture into Trojan and satellite orbits. Various mechanisms for capture into libration were proposed, e.g., increase in Jupiter/Sun mass ratio, change in Jovian orbital radius, and collisions of asteroids with interplanetary dust. Studies include effects of solar nebula gas drag on orbital evolution. In general, the gas deviates from Keplerian motion, causing secular decay of planetesimal orbits, as well as damping eccentricity. The motion of bodies near Jupiter under the effect of a resisting medium was numerically explored. The equations of motion were integrated using the formalism of the planar restricted three body problem, modified to include effects by gas drag and a growing Jupiter.

Weidenschilling, S. J.↗
NASA NTRS1986

Contact dynamics math model

The Space Station Mechanism Test Bed consists of a hydraulically driven, computer controlled six degree of freedom (DOF) motion system with which docking, berthing, and other mechanisms can be evaluated. Measured contact forces and moments are provided to the simulation host computer to enable representation of orbital contact dynamics. This report describes the development of a generalized math model which represents the relative motion between two rigid orbiting vehicles. The model allows motion in six DOF for each body, with no vehicle size limitation. The rotational and translational equations of motion are derived. The method used to transform the forces and moments from the sensor location to the vehicles' centers of mass is also explained. Two math models of docking mechanisms, a simple translational spring and the Remote Manipulator System end effector, are presented along with simulation results. The translational spring model is used in an attempt to verify the simulation with compensated hardware in the loop results.

Glaese, John R.↗
NASA NTRS1992

An analytical evaluation of mascon effects in a semi-analytic theory

A semianalytic method to predict the orbit of a spacecraft orbiting a planet and perturbed by oblateness and a gravity anomaly (mascon) is presented. The Hamiltonian is first expressed in closed form in terms of the nonsingular canonical set of Poincare elements where the mascon is represented by a point-mass. The planet global potential is limited to the second and third harmonics. The mascon potential in harmonics is limited to second degree and first order. The original Lie-Hori method is then applied to transform the canonical equations of motion from the osculating element space to the mean element space. Numerical integration of the new equations is used.

Salama, Ahmed H.↗