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At least 37 records · Page 2

Transient dynamic analysis of high-speed lightly loaded cylindrical roller bearings. 1: Analysis

The governing differential equations of motion for a high speed cylindrical roller bearing are developed under the assumptions that the bearing is isothermal and that the roller tilt and skew are very small. Two sets of differential equations are presented: the first which deals with planar motion of the roller bearing system; and the second which includes the effect of roller skewing. The equations as presented are in a format for programming on a digital computer.

Conry, T. F.↗

Design of a new high-performance pointing controller for the Hubble Space Telescope

A new form of high-performance, disturbance-adaptive pointing controller for the Hubble Space Telescope (HST) is proposed. This new controller is all linear (constant gains) and can maintain accurate 'pointing' of the HST in the face of persistent randomly triggered uncertain, unmeasurable 'flapping' motions of the large attached solar array panels. Similar disturbances associated with antennas and other flexible appendages can also be accommodated. The effectiveness and practicality of the proposed new controller is demonstrated by a detailed design and simulation testing of one such controller for a planar-motion, fully nonlinear model of HST. The simulation results show a high degree of disturbance isolation and pointing stability.

Johnson, C. D.↗

Inclusion of known integrals in the optimal trajectory problem

The classical problem of determination of the rocket trajectory which minimizes mass expenditure during motion between two points in the field of a single gravitating body is analyzed. The known integrals of the system are incorporated into the adjoint equations resulting in a reduction from a seventh-order adjoint system to a third-order adjoint system. The first case which is treated in that of planar motion under specific end conditions. In this case a regularization of the recently derived equations is achieved. The general three-dimensional case is also reduced from a seventh-order adjoint system to a third-order adjoint system. In this case a regularization has not been found.

Burns, R. E.↗

A preliminary study of the attitude control for the Shuttle Tethered Satellite System

The objective of this investigation is to determine the equations of motion governing the attitude of a tethered satellite and subsequently to gain insight toward obtaining an appropriate control law. This study relates the coupling of the rotational dynamics of the satellite with the dynamical system of the Orbiter already constructed. In particular, a simplified approach is utilized to describe the satellite as constrained to planar motion. Modifications to the existing tethered satellite trajectory simulation provide a conceptual study of the satellite's behavior and its effect on the overall system.

Rupp, C. C.↗

Component response to random vibratory motion of the carrier vehicle

Two physical models of component plus supporting substructure are considered. Each model consists of a rigid body attached to a moving base by means of linear springs and viscous dampers. The second model differs from the first in that its dampers are elastically supported. The first model receives the more extensive treatment. Base motion, assumed a random translational motion parallel to a fixed axis, is prescribed only to the extent that the power spectral density (PSD) of its acceleration is given; and, as given, its plot on log-log graph paper is a series of straight line segments, each segment having an extremity in common with the adjacent segment. Closed expressions are given for the mean squares of base acceleration, base velocity, and base displacement. The component is restricted to planar motion and allowed two degrees of freedom, one translational and one rotational. Integral expressions are given for the mean squares of component response variables, the transfer functions essential to mean square computation being available via the equations of motion. Closed expressions are given for mean squares of certain of the response variables for the case wherein the base acceleration PSD is constant.

Tuell, L. P.↗

Study of design and control of remote manipulators. Modeling manipulator arms with distributed flexibility for design and control

The interactions of control system and distributed flexible structural dynamics is explored for mechanical arms. A modeling process using 4 x 4 transfer matrices is described which permits the closed loop response of many current arm configurations to be evaluated. Root locus, frequency response, modal shapes, and time impulse response have all been obtained from the digital computer implementation of this model, which is oriented to arm design and allows for easy variation of the arm configuration through data cards. The model corresponds with experimentally observed natural frequencies with an average error of less than 5% in the first three flexible modes in the seven cases considered. The model was used to explore the limits imposed by structural flexibility on a nondimensionalized two link arm with one and two joints for planar motion.

Book, W. J.↗

The planar dynamics of airships

The forces and moments acting upon a LTA vehicle are considered in order to develop parameters describing planar motion. Similar expressions for HTA vehicles will be given to emphasize the greater complexity of aerodynamic effects when buoyancy effects cannot be neglected. A brief summary is also given of the use of virtual mass coefficients to calculate loads on airships.

Regan, F. J.↗

Circularly polarized inertial wave vectors in rotating fluids

The Navier-Stokes equations for a rotating fluid are harmonically analyzed for planar motion in an infinite half-space. All solutions are shown to be a sum of two inertial wave vectors, one circularly polarized to the left (CPL) and the other circularly polarized to the right (CPR). These basic solutions are therefore presented in the same nomenclature and form as that found useful by experimentalists in analyzing flow data (called 'rotary spectra'). The CPL wave acts counter to the Coriolis force and consequently has a slower phase speed and larger damping than the CPR wave. At resonance (forcing frequency = Coriolis frequency) the CPR wave has an infinite phase speed and no damping and is the important component leading to the singular nature of the solutions for certain boundary conditions. All possible resonant singularities are explicitly shown. The unsteady development of these unbounded (limited space structure), cyclic (no time origin or structure) flows is presented to show that with time structure the resonant singularities evolve in a self-similar manner.

Cogley, A. C.↗

The dynamics and control of large flexible space structures, 2. Part A: Shape and orientation control using point actuators

The equations of planar motion for a flexible beam in orbit which includes the effects of gravity gradient torques and control torques from point actuators located along the beam was developed. Two classes of theorems are applied to the linearized form of these equations to establish necessary conditions for controlability for preselected actuator configurations. The feedback gains are selected: (1) based on the decoupling of the original coordinates and to obtain proper damping, and (2) by applying the linear regulator problem to the individual model coordinates separately. The linear control laws obtained using both techniques were evaluated by numerical integration of the nonlinear system equations. Numerical examples considering pitch and various number of modes with different combination of actuator numbers and locations are presented. The independent model control concept used earlier with a discretized model of the thin beam in orbit was reviewed for the case where the number of actuators is less than the number of modes. Results indicate that although the system is controllable it is not stable about the nominal (local vertical) orientation when the control is based on modal decoupling. An alternate control law not based on modal decoupling ensures stability of all the modes.

Bainum, P. M.↗

On the controllability of a long flexible beam in orbit

The equations of planar motion for a long, flexible free-free beam in orbit are developed and include the effects of gravity-gradient torques and control torques resulting from actuators assumed to be located at specific points along the beam. The control devices are used to control both the orientation as well as the shape of the beam. Application of two classes of theorems to the linearized form of these equations is used to establish necessary and sufficient conditions for controllability for different combinations of number/location of actuators with the number of modes contained in the mathematical model. It is seen that the number of actuators, if properly located, can be less than the number of modes in the system model. A numerical example illustrates the controlled response to an initial perturbation in both pitch angle as well as beam shape.

Bainum, P. M.↗

Planar dynamics of a uniform beam with rigid bodies affixed to the ends

The planar dynamics of a uniform elastic beam subject to a variety of geometric and natural boundary conditions and external excitations were analyzed. The beams are inextensible and capable of small transverse bending deformations only. Classical beam vibration eigenvalue problems for a cantilever with tip mass, a cantilever with tip body and an unconstrained beam with rigid bodies at each are examined. The characteristic equations, eigenfunctions and orthogonality relations for each are derived. The forced vibration of a cantilever with tip body subject to base acceleration is analyzed. The exact solution of the governing nonhomogeneous partial differential equation with time dependent boundary conditions is presented and compared with a Rayleigh-Ritz approximate solution. The arbitrary planar motion of an elastic beam with rigid bodies at the ends is addressed. Equations of motion are derived for two modal expansions of the beam deflection. The motion equations are cast in a first order form suitable for numerical integration. Selected FORTRAN programs are provided.

Storch, J.↗

Experimental study on two-dimensional free-flying robot satellite model

The experimental study on a control method for a free flying space robotic arm was treated by means of a two-dimensional laboratory model. The main target is to develop a new control method for trajectory tracking or target capturing, considering dynamical interaction between the manipulator arm and the base vehicle in space micro-gravity environment. In order to simulate the micro-gravity environment mechanically, a laboratory model of a robot satellite supported on air bearings was developed. The model comprises a base equipped with power and air supplies and a two-link manipulator arm. This model has relatively low gravitational and frictional disturbance in planar motion. An on-line resolved motion rate control scheme with vision feedback is developed for experimenting capture operations. The scheme utilizes the Generalized Jacobian Matrix. In experiment, the acceleration environment of the model is evaluated firstly, then target capture operations are examined. The manipulator can properly chase and capture both a standing target and a moving target in spite of complex satellite/manipulator dynamical interactions. The experimental results confirm the validity of the Generalized Jacobian Matrix concept and the proposed control method.

Umetani, Yoji↗

Adaptive Control of Truss Structures for Gossamer Spacecraft

Neural network-based adaptive control is considered for active control of a highly flexible truss structure which may be used to support solar sail membranes. The objective is to suppress unwanted vibrations in SAFE (Solar Array Flight Experiment) boom, a test-bed located at NASA. Compared to previous tests that restrained truss structures in planar motion, full three dimensional motions are tested. Experimental results illustrate the potential of adaptive control in compensating for nonlinear actuation and modeling error, and in rejecting external disturbances.

Yang, Bong-Jun↗

Adaptive Control of Truss Structures for Gossamer Spacecraft

Neural network-based adaptive control is considered for active control of a highly flexible truss structure which may be used to support solar sail membranes. The objective is to suppress unwanted vibrations in SAFE (Solar Array Flight Experiment) boom, a test-bed located at NASA. Compared to previous tests that restrained truss structures in planar motion, full three dimensional motions are tested. Experimental results illustrate the potential of adaptive control in compensating for nonlinear actuation and modeling error, and in rejecting external disturbances.

Yang Bong-Jun↗

Comparison of Pre- and Post-Flight Estimations of Pitch Damping Coefficients for Unguided Entry Vehicles

Introduction: Pre-flight predictions of pitch damping coefficient (𝐶!!+𝐶!"̇)curves are used in entry simulations to determine flight readiness and if any dynamic remediation strategies are required. Accurate characterization of these pitch damping coefficient curves is crucial for mission success. Historically, pre-flight estimations of these curves are derived experimentally either via ballistic range testing or with 1-degree-of-freedom (DOF) free-or forced-oscillation wind tunnel testing. Methodology:With post-flight best-estimated trajectories, a fitting procedure as described in Karlgaard, et. al. [1] is used to compare pre-and post-flight pitch damping coefficients. This technique relies on an assumed analytical form of the trajectory, a limited 3-DOF representation described in Schoenenbergerand Queen [2], which results in anEuler-Cauchy solution form.This solution assumes constant density,thus limited amplitude multi-peak windows of the trajectory are considered to populate the pitch damping-amplitudes pace. Fig. 1 shows preliminary estimations of the pitch damping coefficients estimated using the post-flight best estimated trajectoryfor MER B, using a3-amplitude-peak window. Important to note is that the Euler-Cauchy solution also assumes planar motion, thus coning or 𝛽contribution is not included. Further,the estimated post-flight pitch damping approximations and the pre-flight predictions shown are effective representations of pitch damping, or the integrated effect of the pitch damping coefficient over one pitch cycle at the corresponding cycle’s peak amplitude. Effective pitch damping coefficient curves provide more intuitive insights about where the vehicle is stable and permits readily processed comparisons between data-sets. It is important to note that most pitch damping curves, such as those reported in aerodatabases and utilized in flight mechanics trajectory simulations, are represented in instantaneous angle-of-attack space distinct from what is presented in Fig 1. The extracted post-flight pitch damping coefficient points show a wide range of values across a narrow band of amplitudes (Fig.1a), albeit centered on the published pre-flight approximation. This also applies to the prediction as a function of Mach in Fig1b, where the post-flight scatter points are centered around the pre-flight predictions, but the pre-flight predictions notably lack data aboveMach 5.Further tuning of the technique, such as changing the number of peaks considered in each stencil, resolving density in higher resolution, and employing more accurate fitting procedures (beyond scipy.curve_fit()), will be performed. PosterFocus:This study will apply this reconstruction method to the as-flown trajectories for the following unguided entry vehicles: MER A, MER B, IRVE3, Phoenix, Insight, Pathfinder, and SIAD. The pitch damping coefficient will be derived from these trajectories and compared with the pre-flight predictions. Comparing across different missions, entry environments, and vehicle geometries can inform where our pre-flight testing methodologies accurately capture the flight dynamics. Results will provide valuable insight into the accuracy of pre-flight predicted pitch damping curves. Beyond that, this method can shed light on how accurate these curves need to be, which can inform uncertainty ranges applied to pre-flight curves for other missions.

pitch damping coefficient↗

A review of some exact solutions to the planar equations of motion of a thrusting spacecraft

With the complexities in computing optimal low thrust trajectories, easily-computed, good sub-optimal trajectories provide both a practical alternative for mission designers and a starting point for optimisation. The present paper collects in one place for easy reference and comparison several exact solutions that have been obtained in the literature over the last few decades: the logarithmic spiral, Pinkham's variant thereof, Forbes spiral, the exponential sinusoid, the case of constant radial thrust, Markopoulos's Keplerian thrust arcs, Lawden's spiral, and the analogous Bishop and Azimov spiral.

low-thrust trajectories electric propulsion solar ↗