Rigorous and formal stability of orbits about an oblate planet.
Idealized point mass motion in axisymmetric gravitational field, discussing orbital stability about oblate planet
Kyner, W. T.↗
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Flap/Lag/Torsion Dynamics of a Uniform, Cantilever Rotor Blade in Hover
The dynamic stability of the flap/lag/torsion motion of a uniform, cantilever rotor blade in hover is calculated. The influence of blade collective pitch, lag frequency, torsional flexibility, structural coupling, and precone angle on the stability is examined. Good agreement is found with the results of an independent analytical investigation.
Johnson, W.↗
Peculiar Behavior of He II Disturbances due to Sloshing Dynamics Driven by Jitter Accelerations Associated with Slew Motion in Microgravity
The mathematical formulation of Dewar container sloshing dynamics when partially filled with superfluid liquid He 11 driven by the gravity jitter acceleration associated with slew motion in a microgravity environment is studied. Numerical computation of the sloshing dynamics is based on the non-inertia container bound co-ordinate, and solving time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. This study discloses the capillary effect of the sloshing dynamics governing the liquid-vapour interface fluctuations driven by the gravity jitter acceleration associated with slew motion, which affects the stability of the fluid system in a microgravity environment. The peculiar behaviour of superfluid helium when reacting to the sloshing dynamics driven by the gravity jitter acceleration associated with slew motion in a microgravity environment is also investigated.
Hung, R. J.↗
Oscillatory Thermocapillary Convection
Stability analysis of thermocapillary convection in rectangular cavities is performed using direct numerical simulation. The influence of the Reynolds number (Re), the fluid Prandtl number (Pr) and cavity aspect ratio (Ar) on the motion is investigated. Neutral stability curves for transition to time-dependent convection are delineated in the Re-Ar plane for fluids with Pr=1.0, 4.4, 6.78, and 10. Several interesting features of these diagrams are discussed. One important conclusion is that Ar(epsilon tau) increases as Pr decreases. Thus large values of both Ar and Re are necessary to induce thermocapillary oscillations for small Pr fluids such as liquid metals and semiconductor melts. Energy analysis is also performed for the oscillatory flow in the neighborhood of critical points in order to gain insight into the mechanisms leading to instability.
Xu, Jieyong↗
A study of the use of experimental stability derivates in the calculation of the lateral disturbed motions of a swept-wing airplane and comparison with flight results
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Bird, John D↗
Stability of a dual-spin satellite with two dampers
The rotational stability of a dual-spin satellite consisting of a main body and a symmetric rotor, both spinning about a common axis, is investigated. The main body is equipped with a spring-mass damper, while a partially filled viscous ring damper is mounted on the rapidly spinning rotor. The effect of fluid motion on the rotational stability of the satellite is calculated, considering the fluid as a single particle moving in a tube with viscous damping. Time constants are obtained by solving approximate equations of motion for the nutation-synchronous and the spin-synchronous modes, and the results are found to agree well with the numerical integrations of the exact equations. A limit cycle may exist for some configurations; the nutation angle tends to increase in such cases.
Alfriend, K. T.↗
Stability and control of maneuvering high-performance aircraft
The stability and control of a high-performance aircraft was analyzed, and a design methodology for a departure prevention stability augmentation system (DPSAS) was developed. A general linear aircraft model was derived which includes maneuvering flight effects and trim calculation procedures for investigating highly dynamic trajectories. The stability and control analysis systematically explored the effects of flight condition and angular motion, as well as the stability of typical air combat trajectories. The effects of configuration variation also were examined.
Stengel, R. F.↗
The Influence of Feedback on the Aeroelastic Behavior of Tilt Proprotor Aircraft Including the Effects of Fuselage Motion
The influence of single loop feedbacks to improve the stability of the system are considered. Reduced order dynamic models are employed where appropriate to promote physical insight. The influence of fuselage freedom on the aeroelastic stability, and the influence of the airframe flexibility on the low frequency modes of motion relevant to the stability and control characteristics of the vehicle were examined.
Curtiss, H. C., Jr.↗
Cage stability analysis for SSME HPOTP bearings
A numerical model of cage motion (CAGEDYN) was used to analyze the stability of bearing cages in the Space Shuttle main engine (SSME) high pressure oxygen turbopump (HPOTP). The stability of existing bearing geometries, as well as perturbations of these geometries, was analyzed for various operating conditions. Results of the analyses show that some combinations of operating parameters, exacerbated by the sparse lubrication that exist in the HPOTP bearings, can cause unstable cage oscillations. Frequencies of cage oscillations were predicted by the CAGEDYN numerical model by Fourier analysis of predicted cage motions. Under conditions that cause unstable cage motion, high frequency oscillations were predicted that could cause premature cage failures.
Merriman, T. L.↗
Modeling and Simulation of a Helicopter Slung Load Stabilization Device
This paper addresses the problem of simulation and stabilization of the yaw motions of a cargo container slung load. The study configuration is a UH-60 helicopter carrying a 6ft x 6 ft x 8 ft CONEX container. This load is limited to 60 KIAS in operations and flight testing indicates that it starts spinning in hover and that spin rate increases with airspeed. The simulation reproduced the load yaw motions seen in the flight data after augmenting the load model with terms representing unsteady load yaw moment effects acting to reinforce load oscillations, and augmenting the hook model to include yaw resistance at the hook. The use of a vertical fin to stabilize the load is considered. Results indicate that the CONEX airspeed can be extended to 110 kts using a 3x5 ft fin.
Cicolani, Luigi S.↗
Stability of Intershaft Squeeze Film Dampers
Intershaft squeeze film dampers were investigated for damping of dual rotor aircraft jet engines. It was thought that the intershaft damper would enhance the stability of the rotor-bearing system. Unfortunately, it was determined that the intershaft squeeze film damper was unstable above the engine's first critical speed. Here, a stability analysis of rotors incorporating intershaft squeeze film dampers is discussed. A rotor model consisting of two Jeffcott rotors with two intershaft squeeze film dampers was investigated. Examining the system characteristic equation for the conditions at which the roots indicate an ever-growing unstable motion results in the stability conditions. The cause of the instability is identified as the rotation of the oil in the damper clearance. Several proposed configurations of intershaft squeeze film dampers are discussed, and it is shown that the intershaft dampers are stable supercritically only with a configuration in which the oil film does not rotate.
El-Shafei, A.↗
A method for the Liapunov stability analysis of hybrid dynamical systems possessing ignorable coordinates
Liapunov stability analysis of dynamic systems described by simultaneous ordinary and partial differential equations of motion, applying to satellite spin stabilization
Meirovitch, L.↗
Asymmetrical booster ascent guidance and control system design study. Volume 1: Summary
Dynamics and control, stability, and guidance analyses are summarized for the asymmetrical booster ascent guidance and control system design studies, performed in conjunction with space shuttle planning. The mathematical models developed for use in rigid body and flexible body versions of the NASA JSC space shuttle functional simulator are briefly discussed, along with information on the following: (1) space shuttle stability analysis using equations of motion for both pitch and lateral axes; (2) the computer program used to obtain stability margin; and (3) the guidance equations developed for the space shuttle powered flight phases.
Williams, F. E.↗
Stability of rotating magnetic stars and planets as Jupiter and the origin of convective motion
Based on the method of the energy principle, the effect of the coriolis force on the stability of rotating hydromagnetic systems was examined and the condition for instability was derived. It is shown that, in rotating systems, the coriolis force inhibits the onset of convective motion and that, once the condition for instability is fulfilled, overstable states are produced with respect to this motion. Such states seem to affect the onset of turbulent convective motion.
Sakurai, K.↗
Long-term risk analysis associated with nuclear waste disposal in space
An assessment and verification of previous analytic results on the long term risk of earth reentry for hazardous payloads is presented. The two areas were studied: (1) stability of nominal, near-circular storage orbits in the regions between Venus and earth and between earth and Mars, and (2) probability of earth reentry for off-nominal planet-crossing orbits resulting from deployment system failures. In the first area, numerical integrations of the equations of motion are compared with stability predications based on secular perturbation theory. The agreement is good in terms of the heliocentric distances covered and the general behavior of the orbital history, although certain near-resonance situations can lead to difficulty. In the second area, a Monte Carlo simulation of orbital evolution is used and the results compared with Opik's analytic theory of planetary encounters and collision statistics, with data verified to within a close order-of-magnitude.
Friedlander, A. L.↗
Modeling and Analysis of Large Amplitude Flight Maneuvers
Analytical methods for stability analysis of large amplitude aircraft motion have been slow to develop because many nonlinear system stability assessment methods are restricted to a state-space dimension of less than three. The proffered approach is to create regional cell-to-cell maps for strategically located two-dimensional subspaces within the higher-dimensional model statespace. These regional solutions capture nonlinear behavior better than linearized point solutions. They also avoid the computational difficulties that emerge when attempting to create a cell map for the entire state-space. Example stability results are presented for a general aviation aircraft and a micro-aerial vehicle configuration. The analytical results are consistent with characteristics that were discovered during previous flight-testing.
Anderson, Mark R.↗
Active Debris Removal - A Grand Engineering Challenge for the Twenty-First Century
The collision between Iridium 33 and Cosmos 2251 in 2009 underlined the potential of an ongoing collision cascade effect (the Kessler Syndrome ) in the near-Earth orbital debris environment. A 2006 NASA analysis of the instability of the debris population in the low Earth orbit (LEO, the region below 2000 km altitude) shows that the environment has reached a point where the debris population will continue to increase in the next 200 years, even without any future launches. The increase is driven by fragments generated via collisions among existing objects in LEO. In reality, the situation will be worse than this prediction because satellite launches will continue and unexpected major breakups may continue to occur. Mitigation measures commonly adopted by the international space community (such as the 25-year rule) will help, but will be insufficient to stop the population growth. To better preserve the near-Earth space environment for future generations, active debris removal (ADR) should be considered. The idea of active debris removal is not new. However, due to the monumental technical, resource, operational, legal, and political challenges associated with removing objects from orbit, it has not yet been widely considered feasible. The recent major breakup events and the environment modeling efforts have certainly reignited the interest in using active debris removal to remediate the environment. This trend is further highlighted by the National Space Policy of the United States of America, released by the White House in June 2010, where the President explicitly directs NASA and the Department of Defense to pursue research and development of technology and techniques, to mitigate and remove on-orbit debris, reduce hazards, and increase understanding of the current and future debris environment. A 2009 modeling study by the NASA Orbital Debris Program Office has shown that, in order to maintain the LEO debris population at a constant level for the next 200 years, an active debris removal of about five objects per year is needed. The targets identified for removal are those with the highest mass and collision probability products. Analyses from the study indicate that the majority of those objects are spent upper stages with masses ranging from 1 to more than 8 metric tons, residing in several altitude regions and concentrated in about 10 inclination bands. To remove five of those objects per year in a cost-effective manner truly represents a grand challenge in engineering and technology development. An end-to-end debris removal operation includes, in general terms, launches orbit rendezvous, precision tracking, stabilization (of the tumbling motion), capture, and deorbit of the targets. An ADR system deigned to remove a single object is not very cost-effective. Therefore, the repeatability of the removal system is almost a requirement. Some of the technologies involved in the ADR process do exist, but the difficulty is to make them more cost effective. Other technologies, such as ways to stabilize a massive tumbling upper stage and the capture mechanisms, are new and will require major innovative research and development efforts. This paper summarizes an updated assessment of the environment, including what needs to be done to control the population growth, and outlines the major engineering and technology challenges to carry out active debris removal to preserve the environment.
Liou, Jer-Chyi↗
Transonic Correction Method for Flight Dynamic Stability Analysis of Mach 0.745 Transonic Truss-Braced Wing
This paper presents a transonic correction method for obtaining dynamic stability derivatives for flight dynamic stability analysis. The method provides a transonic correction to the Theodorsen's theory of unsteady aerodynamics using FUN3D CFD solver of unsteady Reynolds-averaged Navier-Stokes equations (RANS) for a series of wing sections of the Mach 0.745 Transonic Truss-Braced Wing in pitch and plunge oscillations. Unsteady lift and pitching moment coefficients are obtained and used to develop the correction terms in the Theodorsen's theory to account for transonic aerodynamics. The unsteady lift and pitching moment derivatives with respect to the unsteady angle of attack are obtained as frequency response functions of the reduced frequency. These frequency response functions are used to compute the dynamic stability derivatives of lift and pitching moment due to the angle of attack and pitch rate and the dynamic stability derivatives for the rolling moment and yawing moment with respect to the roll rate and yaw rate. A transonic correction is applied to steady-state stability derivatives computed by VSPAERO solver using transonic small disturbance code TSFOIL coupled to an integral boundary method. A dynamic stability analysis is conducted for longitudinal and lateral-directional motions. Without transonic corrections and dynamic stability derivatives, the analysis indicates an unstable phugoid mode. The transonic correction applied to the steady-state stability derivatives computed by VSPAERO shows a stable phugoid mode. This is due to the increase of the drag stability derivatives as a result of the additional wave drag contribution in transonic flow. The effect of the transonic dynamic stability derivatives is observed to be a significant contributor to the increase in the damping values of all the flight dynamic modes of the Mach 0.745 Transonic-Truss Braced Wing.
Transonic↗