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Results for “EQUATIONS OF 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.

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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Application of Navier-Stokes analysis to stall flutter

A solution procedure was developed to investigate the two-dimensional, one- or two-dimensional flutter characteristics of arbitrary airfoils. This procedure requires a simultaneous integration in time of the solid and fluid equations of motion. The fluid equations of motion are the unsteady compressible Navier-Stokes equations, solved in a body-fitted moving coordinate system using an approximate factorization scheme. The solid equations of motion are integrated in time using an Euler implicit scheme. Flutter is said to occur if small disturbances imposed on the airfoil attitude lead to divergent oscillatory motions at subsequent times. The flutter characteristics of airfoils in subsonic speed at high angles of attack and airfoils in high subsonic and transonic speeds at low angles of attack are investigated. The stall flutter characteristics are also predicted using the same procedure.

Wu, J. C.↗
NASA NTRS1979

Documentation of the Fourth Order Band Model

A general circulation model is presented which uses quadratically conservative, fourth order horizontal space differences on an unstaggered grid and second order vertical space differences with a forward-backward or a smooth leap frog time scheme to solve the primitive equations of motion. The dynamic equations for motion, finite difference equations, a discussion of the structure and flow chart of the program code, a program listing, and three relevent papers are given.

Kalnay-Rivas, E.↗
NASA NTRS1976

The singly averaged differential equations of satellite motion for e greater than or equal to 0 and less than 1

The singly-averaged differential equations of motion of a satellite are developed in terms of parameters valid for all eccentricities less than one. The perturbations included in the acceleration model are due to an aspherical central planet (zonal harmonics up to degree 20 and resonant harmonics up to degree and order 20), atmospheric drag for a time-varying atmosphere, third-body gravity (the sun and moon for an earth satellite), solar radiation pressure with shadowing, and impulsive maneuvers. Analytic averaging is used to remove short-period terms due to the aspherical central planet and third-body gravity. Numerical averaging is used to remove short-period terms due to atmospheric drag and solar radiation pressure.

Dallas, S. S.↗
NASA NTRS1983

A short cut integration scheme to determine the dynamic response of a launch vehicle with several payloads

The coupled base motion equations of a system composed of a launch vehicle and several payloads are derived. In previous work it was shown how the special form of these equations allow for a quick and accurate solution both for the response and the loads of the system. In this paper a short-cut version of this direct integration technique is presented and evaluated. The result is a method which, depending on the nature of the structure at hand, vasilates between a full-scale coupled base motion approach and an open loop base drive method. Although completely general, the presented technique is most effective when the number of interface degrees of freedom is relatively small compared to the overall number of degrees of freedom of the system. The S.T.S.-S.T.-O.M.S. Kit system is used as an illustrative example.

Engels, R. C.↗
NASA NTRS1996

Numerical Modeling of Spray Combustion with an Unstructured-Grid Method

The present unstructured-grid method follows strictly the basic finite volume forms of the conservation laws of the governing equations for the entire flow domain. High-order spatially accurate formulation has been employed for the numerical solutions of the Navier-Stokes equations. A two-equation k-epsilon turbulence model is also incorporated in the unstructured-grid solver. The convergence of the resulted linear algebraic equation is accelerated with preconditioned Conjugate Gradient method. A statistical spray combustion model has been incorporated into the present unstructured-grid solver. In this model, spray is represented by discrete particles, rather than by continuous distributions. A finite number of computational particles are used to predict a sample of total population of particles. Particle trajectories are integrated using their momentum and motion equations and particles exchange mass, momentum and energy with the gas within the computational cell in which they are located. The interaction calculations are performed simultaneously and eliminate global iteration for the two-phase momentum exchange. A transient spray flame in a high pressure combustion chamber is predicted and then the solution of liquid-fuel combusting flow with a rotating cup atomizer is presented and compared with the experimental data. The major conclusion of this investigation is that the unstructured-grid method can be employed to study very complicated flow fields of turbulent spray combustion. Grid adaptation can be easily achieved in any flow domain such as droplet evaporation and combustion zone. Future applications of the present model can be found in the full three-dimensional study of flow fields of gas turbine and liquid propulsion engine combustion chambers with multi-injectors.

Shang, H. M.↗
NASA NTRS1975

An optimal control of a flexible spinning satellite

A modification of optimal spinning satellite control theory is proposed, based on introducing an additional vector into the equation for control torque components. This modification essentially means that the amplitudes of the time-dependent satellite perturbation functions can be made small when the amplitudes of the control torque components are allowed to be different. An algorithm for computer simulation of the satellite control theory is provided. A singular perturbation scheme is used which greatly reduces the number of degrees of freedom in the flexible satellite motion equations.

Das, A.↗
NASA NTRS1975

The motion of throw away detectors relative to the space shuttle

The motions of throw away detectors (TAD's) are analyzed using the linearized relative motion equations. The TAD's are to be used in the amps program as diagnostic instruments for making various measurements near the shuttle. The TAD's are ejected from the shuttle in arbitrary directions with small relative velocities (0.1 to 1.0 m/s) their subsequent trajectories relative to the shuttle are analyzed. Initial conditions that are likely to result in recontact between the TAD and the shuttle are identified. The sensitivity of the motion to variations in the initial conditions, possibly resulting from inaccuracy in the ejection mechanism, are analyzed as are effects of atmospheric drag. A targeting method, a method of giving the TAD correct initial conditions such that it will pass through a given point relative to the shuttle at a given time, is developed. The results of many specific cases are presented in graphical form.

Mullins, L. D.↗
NASA NTRS1979

Equation modifying program, L219 (EQMOD). Volume 1: Engineering and usage

The analysis and use of the Equation Modifying Program (EQMOD) L219, digital computer program which modifies matrices according to specific instructions was described. The program modifies the theoretical equation of motion and load equations generated by the DYLOFLEX programs Equation of Motion L217 (EOM), and Load Equations, L218 (LOADS), respectively.

Miller, R. D.↗
NASA NTRS1984

Incorporation of wind shear terms into the governing equations of aircraft motion

Conventional analyses of aircraft motion in the atmosphere have neglected wind speed variability on the scales associated with many atmospheric phenomena such as thunderstorms, low-level jets, etc. These phemonena produce wind shears that have been determined as the probable cause in many recent commercial airline accidents. This paper derives the six degrees equations of motion or an aircraft incorporating the variable wind terms. The equations are presented in several coordinate systems (i.e., body coordinates, inertial coordinates, etc.). The wind shear terms, including the temporal and spatial gradients of the wind, appear differently in the various coordinate system. These terms are discussed. Also, the influence of wind shear on inputs to computing the aerodynamic coefficients such as the effects of wind velocity vector rotation on relative angular rates of rotation and on the time rate of change of angles of attack and side slip are addressed.

Frost, W.↗
DOE OSTI2020

Dynamic Response of a Semiactive Suspension System with Hysteretic Nonlinear Energy Sink Based on Random Excitation by means of Computer Simulation

This paper aims to investigate the property and behavior of the hysteretic nonlinear energy sink (HNES) coupled to a half vehicle system which is a nine-degree-of-freedom, nonlinear, and semiactive suspension system in order to improve the ride comfort and increase the stability in shock mitigation by using the computer simulation method. The HNES model is a semiactive suspension device, which comprises the famous Bouc–Wen (B-W) model employed to describe the force produced by both the purely hysteretic spring and linear elastic spring of potentially negative stiffness connected in parallel, for the half vehicle system. Nine nonlinear motion equations of the half vehicle system are derived in terms of the seven displacements and the two dimensionless hysteretic variables, which are integrated numerically by employing the direct time integration method for studying both the variables of vertical displacements, velocities, accelerations, chassis pitch angle, and the ride comfort and driver safety, respectively, based on the bump and random road inputs of the pseudoexcitation method as excitation signal. Simulation results show that, compared with the HNES model and the magnetorheological (MR) model coupled to the half vehicle system, the ride comfort and stability have been evidently improved. A successful validation process has been performed, which indicated that both the ride comfort and driver safety properties of the HNES model coupled to half vehicle significantly improved.

Chen, Hui↗
DOE OSTI2025

Scrambling Dynamics with Imperfections in a Solvable Model

We study how probes of quantum scrambling dynamics respond to two kinds of imperfections -- unequal forward and backward evolutions and decoherence -- in a solvable Brownian circuit model. We calculate a ``renormalized'' out-of-time-order correlator (ROTOC) in the model with $N$ qubits, and we show that the circuit-averaged ROTOC is controlled by an effective probability distribution in operator weight space which obeys a system of $N$ non-linear equations of motion. These equations can be easily solved numerically for large system sizes which are beyond the reach of exact methods. Moreover, for an operator initially concentrated on weight one $w_0=1$, we provide an exact solution to the equations in the thermodynamic limit of many qubits that is valid for all times, all non-vanishing perturbation strengths $p\gtrsim 1/\sqrt{N}$, and all decoherence strengths. We also show that a generic initial condition $w_0 >1$ leads to a metastable state that eventually collapses to the $w_0=1$ case after a lifetime $\sim \log(N/w_0)$. Our results highlight situations where it is still possible to extract the unperturbed chaos exponent even in the presence of imperfections, and we comment on the applications of our results to existing experiments with nuclear spins and to future scrambling experiments.

FOS: Physical sciences↗
NASA NTRS1962

LIFT CONTROL DURING ATMOSPHERE ENTRY FROM SUPERCIRCULAR VELOCITY

This paper presents an analysis of a guidance method which uses a reference trajectory. The four state variables needed to prescribe the trajectory are used as follows : Velocity is made the independent variable, and the errors in the rate-of-climb, acceleration, and range variables away from the reference are used to govern the lift. A linearized form of the motion equations is used to show that this represents a third-order control system. First- and second- order control terms (rate of climb and acceleration inputs) are shown to determine the entry corridor depth by stabilizing the trajectory so that the vehicle does not skip back out of the atmosphere or does not exceed a specified acceleration limit. The destabilizing effect that range input (the third-order control term) can have is illustrated and the results indicate that a low value of range input gain must be used at the high supercircular velocities while larger values of range input gain can be used at lower velocities. The usable corridor depth and range capability with this guidance system are demonstrated for a lifting capsule (L/D = 0.5). The practical applications of this system are illustrated with a fixed trim configuration wherein roll angle is used to command the desired lift. The results show that the guidance system requires only one reference trajectory for abort entry conditions as well as for entry conditions near the design values.

Atmosphere↗
NASA NTRS1963

Spring separation of spacecraft

IBM 7090 digital computer program for solving equations of motion for spacecraft separating from final rocket stage or another spacecraft by means of precision helical compression springs

SPACECRAFT CONFIGURATION↗