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NASA NTRS2003

Preliminary Planar Formation: Flight Dynamics Near Sun-Earth L2 Point

NASA's Goddard Space Flight Center is planning a series of missions in the vicinity of the Sun-Earth L2 libration point. Some of these projects will involve a distributed space system of telescope spacecraft acting together as a single telescope for high-resolution. The individual telescopes will be configured in a plane, surrounding a hub, where the telescope plane can be aimed toward various astronomical targets of interest. In preparation for these missions, it is necessary to develop an improved understanding of the dynamical behavior of objects in a planar configuration near L2. The classical circular restricted three body problem is taken as the basis for the analysis. At first order, the motion of such a telescope relative to the hub is described by a system of linear second order differential equations. These equations are identical to the circular restricted problem's linear equations describing the hub motion about L2. Therefore, the fundamental frequencies, both parallel to and normal to the ecliptic plane, are the same for the relative telescope motion as for the hub motion. To maintain the telescope plane for the duration necessary for the planned observations, a halo-type orbit of the telescopes about the hub is investigated. By using a halo orbit, the individual telescopes remain in approximately the same plane over the observation duration. For such an orbit, the fundamental periods parallel to and normal to the ecliptic plane are forced to be the same by careful selection of the initial conditions in order to adjust the higher order forces. The relative amplitudes of the resulting oscillations are associated with the orientation of the telescope plane relative to the ecliptic. As in the circular restricted problem, initial conditions for the linearized equations must be selected so as not to excite the convergent or divergent linear modes. In a higher order analysis, the telescope relative motion equations include the effects of the position of the hub relative to L2. In this paper, the differential equations are developed through second order in the distance of the hub from the libration point. A modified Lindstedt-Poincad perturbation method is employed to construct the solution of these differential equations through that same order of magnitude. In the course of the solution process, relationships are determined between the initial conditions of the telescopes, selected in order to avoid resonance excitation. As the differential equations include the hub position, it is necessary to simultaneously develop the solution for the hub. As has been done in past analyses of the circular restricted problem, the hub position is written in a power series formulation in terms of its distance from L2. Then, in order to be included in the telescope equations, the hub solution is cast in terms of the nonlinear frequency of the relative telescope motion. In the course of the analysis, it is determined that the hub should also maintain a halo orbit - about L2. Additionally, relationships are formed between the initial conditions of the telescopes and the hub. These relationships may be used to associate sets of initial conditions with particular orientations of the telescope plane. The accuracy of the analytical solution is verified through various simulations and comparison to numerical integration of the differential equations. The results of the simulations are presented, along with a graphical representation of the relationships between the initial conditions of the telescopes and hub.

Segerman, Alan M.↗

NASA NTRS1993

Design considerations for ultra-precision magnetic bearing supported slides

Development plans for a prototype servocontrolled machine with 1 angstrom resolution of linear motion and 50 mm range of travel are described. Two such devices could then be combined to produce a two dimensional machine for probing large planar objects with atomic resolution, the Angstrom Resolution Measuring Machine (ARMM).

Slocum, Alexander H.↗

NASA NTRS2006

Approximations of distant retrograde orbits for mission design

Distant retrograde orbits (DROs) are stable periodic orbit solutions of the equations of motion in the circular restricted three body problem. Since no closed form expressions for DROs are known, we present methods for approximating a family of planar DROs for an arbitrary, fixed mass ratio. Furthermore we give methods for computing the first and second derivatives of the position and velocity with respect to the variables that parameterize the family. The approximation and derivative methods described allow a mission designer to target specific DROs or a range of DROs with no regard to phasing in contrast to the more limited case of targeting a six-state only.

Distant Retrograde Orbits (DRO)↗

NASA NTRS1989

Manipulators with flexible links: A simple model and experiments

A simple dynamic model proposed for flexible links is briefly reviewed and experimental control results are presented for different flexible systems. A simple dynamic model is useful for rapid prototyping of manipulators and their control systems, for possible application to manipulator design decisions, and for real time computation as might be applied in model based or feedforward control. Such a model is proposed, with the further advantage that clear physical arguments and explanations can be associated with its simplifying features and with its resulting analytical properties. The model is mathematically equivalent to Rayleigh's method. Taking the example of planar bending, the approach originates in its choice of two amplitude variables, typically chosen as the link end rotations referenced to the chord (or the tangent) motion of the link. This particular choice is key in establishing the advantageous features of the model, and it was used to support the series of experiments reported.

Shimoyama, Isao↗

NASA NTRSDate not supplied

Additively Printed Flexible Temperature Sensor for Wearable Applications

The flexible sensor has the capability to be mounted on any curved surfaces of applications and be used for portable devices. Additively printed sensors have received attention owing to their compact design and ability of application to non-planar surfaces. Wearable applications require capability of integration into a variety of surfaces with ability to flex, fold, twist and stretch under the stresses of daily motion. There is scarcity of data on the interaction of the process parameters with the realized performance. In addition, there is need for data focused on sensor accuracy, repeatability, and reliability. In this study, experimental analysis on function of the fabricated sensing board is conducted. The temperature sensors are made by direct write printing method with nScrypt printer. A calibration of the sensors has been conducted to confirm that resistance is well related to actual temperature and find TCR (temperature coefficient to resistance). The evolution of resistance has been correlated with the environmental temperature. The sensor hysteresis has been quantified using upswing and downswing of the environmental temperature. In addition, the effect of humidity on the temperature sensor accuracy and performance has been quantified. The effect of a polymide coat on the sensor to prevent humidity effects has also been quantified.

Pradeep Lall↗

NASA NTRS1985

Drag characteristics of unsteady, perturbed boundary layer flows

A series of time-dependent numerical computations have been performed for the flow of an unsteady boundary layer over an embedded cavity, which is aligned normal to the flow direction. The unsteady flow is the result of the imposition of a Stuart vortex, at the inflow boundary of the computational domain, onto an otherwise unperturbed two-dimensional laminar boundary layer flow. This produces a strongly vortical, but spatially monochromatic, motion at inflow which is allowed to evolve downstream through the time-dependent numerical solution of appropriate conservation equations. As the imposed vortex evolves over the solid boundary, a weaker induced vortical motion is produced and together these perturbing motions interact with the fluid motion in the embedded cavity. An analysis of the pertinent dynamic variables as well as the time-dependent drag characteristics for this type of non-planar geometry is performed; with particular emphasis on the relative contribution of both pressure drag and frictional drag at various times in the evolution process.

Gatski, T. B.↗

NASA NTRS1995

A Combined Geometric Approach for Computational Fluid Dynamics on Dynamic Grids

A combined geometric approach for computational fluid dynamics is presented for the analysis of unsteady flow about mechanisms in which its components are in moderate relative motion. For a CFD analysis, the total dynamics problem involves the dynamics of the aspects of geometry modeling, grid generation, and flow modeling. The interrelationships between these three aspects allow for a more natural formulation of the problem and the sharing of information which can be advantageous to the computation of the dynamics. The approach is applied to planar geometries with the use of an efficient multi-block, structured grid generation method to compute unsteady, two-dimensional and axisymmetric flow. The applications presented include the computation of the unsteady, inviscid flow about a hinged-flap with flap deflections and a high-speed inlet with centerbody motion as part of the unstart / restart operation.

Slater, John W.↗

NASA NTRS1989

Development and application of a program to calculate transonic flow around an oscillating three-dimensional wing using finite difference procedures

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. Difference equations are derived for harmonic transonic flow to include a coordinate transformation for swept and tapered planforms. A pilot program is developed for three-dimensional planar lifting surface configurations (including thickness) for the CRAY-XMP at Boeing Commercial Airplanes and for the CYBER VPS-32 at the NASA Langley Research Center. An investigation is made of the effect of the location of the outer boundaries on accuracy for very small reduced frequencies. Finally, the pilot program is applied to the flutter analysis of a rectangular wing.

Weatherill, Warren H.↗

NASA NTRS1992

The evolution of line-tied coronal arcades including a converging footpoint motion

It has been demonstrated in the past that single, 2D coronal arcades are very unlikely driven unstable by a simple shear of the photospheric footpoints of the magnetic field lines. By means of 2D, time-dependent MHD simulations, evidence is presented that a resistive instability can result if in addition to the footpoint shear a slow motion of the footpoints toward the photospheric neutral line is included. The photospheric footpoint velocity in this model is nonsingular and the shear dominates everywhere. Starting from a planar potential field geometry for the arcade, it is found that after some time a current sheet is formed which is unstable with respect to the tearing instability. The time of its onset scales with the logarithm of the magnetic diffusivity assumed in the calculation. In its nonlinear phase, a quasi-stationary situation arises in the vicinity of the x-line with an almost constant reconnection rate. The height of the x-line above the photosphere and the distance of the separatrix footpoints remain almost constant in this phase, while the helical flux tube, formed above the neutral line, continuously grows in size.

Inhester, B.↗

NASA NTRS1983

Instabilities of dynamic thermocapillary liquid layers. I Convective instabilities

A steady shear flow is set up in a planar liquid layer bounded below by a rigid plate, and above by an interface with a passive gas, by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. The thermal-convective instabilities to which this dynamic state is susceptible include stationary longitudinal rolls involving the classical Marangoni instability, and unsteady hydrothermal waves, whose new instability mechanism derives its energy from the horizontal temperature gradients. The thermal stability characteristics for liquid layers with and without return flow profiles are presently given as functions of the Prandtl number for the liquid and the Biot number for the interface, and comparisons are made with available experimental observations.

Smith, M. K.↗

NASA NTRS1990

Simulations of gas clouds in interacting galaxies

A companion can induce a variety of morphological changes in a galaxy. The author uses N-body simulations to study the effects of different kinds of perturbations on the dynamics of a disk galaxy. The model is two-dimensional, with a disk consisting of about 60,000 particles. Most of the particles (80%) represent the old stellar population with a high velocity dispersion, while the rest (20%) represent gas clouds with a low velocity dispersion. Initially, the velocity dispersion corresponds to Q = 1 for the star particles, and Q = O for the gas particles, where Q is Toomre's (1964) stability parameter. The gas clouds can collide inelastically. The disk is stabilized by a rigid halo potential, and by the random motions of the old star particles. To simulate the effect of an encounter on the disk, a companion galaxy, modelled as a point mass, can move in a co-planar orbit around the disk. A complete description of the N-body code is found in Thomasson (1989). The spiral structures caused by a companion in first a direct and then a retrograde (with respect to the rotation of the disk) parabolic orbit are presented. The associated velocity fields suggest a way to observationally distinguish between leading and trailing spiral arms. The stability of the gas component in a disk in which tidally triggered infall of gas to the center occurs is studied. Finally, the author shows how a ring of gas can form in a disk as a result of a co-planar encounter with another galaxy.

Thomasson, Magnus↗

NASA NTRS2011

Planar Rotary Piezoelectric Motor Using Ultrasonic Horns

A motor involves a simple design that can be embedded into a plate structure by incorporating ultrasonic horn actuators into the plate. The piezoelectric material that is integrated into the horns is pre-stressed with flexures. Piezoelectric actuators are attractive for their ability to generate precision high strokes, torques, and forces while operating under relatively harsh conditions (temperatures at single-digit K to as high as 1,273 K). Electromagnetic motors (EM) typically have high rotational speed and low torque. In order to produce a useful torque, these motors are geared down to reduce the speed and increase the torque. This gearing adds mass and reduces the efficiency of the EM. Piezoelectric motors can be designed with high torques and lower speeds directly without the need for gears. Designs were developed for producing rotary motion based on the Barth concept of an ultrasonic horn driving a rotor. This idea was extended to a linear motor design by having the horns drive a slider. The unique feature of these motors is that they can be designed in a monolithic planar structure. The design is a unidirectional motor, which is driven by eight horn actuators, that rotates in the clockwise direction. There are two sets of flexures. The flexures around the piezoelectric material are pre-stress flexures and they pre-load the piezoelectric disks to maintain their being operated under compression when electric field is applied. The other set of flexures is a mounting flexure that attaches to the horn at the nodal point and can be designed to generate a normal force between the horn tip and the rotor so that to first order it operates independently and compensates for the wear between the horn and the rotor.

Sherrit, Stewart↗

NASA NTRS1990

Performance limitations of joint variable-feedback controllers due to manipulator structural flexibility

The performance limitations of manipulators under joint variable-feedback control are studied as a function of the mechanical flexibility inherent in the manipulator structure. A finite-dimensional time-domain dynamic model of a two-link two-joint planar manipulator is used in the study. Emphasis is placed on determining the limitations of control algorithms that use only joint variable-feedback information in calculations of control decisions, since most motion control systems in practice are of this kind. Both fine and gross motion cases are studied. Results for fine motion agree well with previously reported results in the literature and are also helpful in explaining the performance limitations in fast gross motions.

Cetinkunt, Sabri↗

NASA NTRS2005

Deformation and Flexibility Equations for ARIS Umbilicals Idealized as Planar Elastica

The International Space Station relies on the active rack isolation system (ARIS) as the central component of an integrated, stationwide strategy to isolate microgravity space-science experiments. ARIS uses electromechanical actuators to isolate an international standard payload rack from disturbances due to the motion of the Space Station. Disturbances to microgravity experiments on ARIS isolated racks are transmitted primarily via the ARIS power and vacuum umbilicals. Experimental tests indicate that these umbilicals resonate at frequencies outside the ARIS controller s bandwidth at levels of potential concern for certain microgravity experiments. Reduction in the umbilical resonant frequencies could help to address this issue. This work documents the development and verification of equations for the in-plane deflections and flexibilities of an idealized umbilical (thin, flexible, inextensible, cantilever beam) under end-point, in-plane loading (inclined-force and moment). The effect of gravity is neglected due to the on-orbit application. The analysis assumes an initially curved (not necessarily circular), cantilevered umbilical with uniform cross-section, which undergoes large deflections with no plastic deformation, such that the umbilical slope changes monotonically. The treatment is applicable to the ARIS power and vacuum umbilicals under the indicated assumptions.

Hampton, R. David↗

NASA NTRS1972

Computer program for calculating laminar and turbulent boundary layer development in compressible flow

A computer program is described which performs a numerical integration of the equations of motion for a compressible two-dimensional boundary layer. Boundary layer calculations may be carried out for both laminar and turbulent flow for arbitrary Reynolds number and free stream Mach number distribution on planar or axisymmetric bodies with wall heating or cooling, longitudinal wall curvature, wall suction or blowing, and a rough or a smooth wall. A variety of options are available as initial conditions. The program can generate laminar initial conditions such as Falkner-Skan similarity solutions (so that initial wedge flows can be simulated including Blasius or stagnation point flow) or approximate equilibrium turbulent profiles. Alternatively, initial profile input data can be utilized.

Herring, H. J.↗

NASA NTRS1987

The electron distribution function upstream from the earth's bow shock

A general analytic theory for the distribution function of particles backstreaming from an arbitrary shock in a magnetized plasma is presented. Particle motions are shown to be restricted to two-dimensional planes. A general form for the source term describing upstreaming particles accelerated at the shock is presented along with explicit source terms for planar and parabolic shocks. The origin and form of the escape velocity cutoff for a shock in a magnetized plasma are discussed. The distribution function upstream of a finite planar shock and a parabolic shock in two dimensions is calculated, and an analytic approximation of the cutoff velocity at points in the upstream region is derived. The theory is then applied to the earth's bow shock, calculating distribution functions and the nature and spatial variation of the cutoff velocity. The theory for the particle distribution upstream of the bow shock is compared with the model of Filbert and Kellogg (1979).

Cairns, Iver H.↗

NASA NTRS1992

Asteroid-type orbit evolution near the 5:2 resonance

In this case of the 5:2 commensurability with the motion of Jupiter, an asteroid can reach the orbits of Mars, Earth, and Venus when eccentricity e is greater than 0.41, 0.65, and 0.74, respectively. For individual fictitious asteroids, Ipatov and Yoshikawa obtained a growth in e from 0.15 to 074-0.76. Rates of changes in orbital orientations are different for Mars, Earth, Venus, and the asteroid. Therefore, for corresponding values of e, the asteroid could encounter these planets and leave the gap at those encounters. In order to investigate this hypothesis of the 5:2 Kirkwood gap formation, Ipatov studied the regions of initial data for which the eccentricities of asteroids located near the 5:2 commensurability exceeded 0.41 during evolution. The orbit evolution for 500 fictitious asteroids was investigated by numerical integration of the complete (unaveraged) equations of motion for the three-body problem (Sun-Jupiter-asteroid). The equations of motion were integrated in the time intervals T is greater than or equal to 5(10)(exp 3)t(sub J) (t(sub J) is the heliocentric orbital period of Jupiter) in the planar model, T is greater than or equal to 10(exp 4)t(sub J) at initial inclination 5 deg is less than or equal to i(sub 0) is less than or equal to 20 deg and T = 10(exp 5)t(sub J) at i(sub 0) = 40 deg. The larger interval T was taken at i(sub 0) = 40 deg because in this case for the majority of runs maximum values of e and i were reached in the time delta(t) is greater than 2(10)(exp 4)t(sub J).

Ipatov, S. I.↗

NASA NTRS1979

Effects of tether attachments on the Shuttle/Tethered Satellite System dynamics

The dynamics of the Shuttle Tethered Satellite System are influenced by attaching the tether at some point other than the center-of-masses of the Shuttle and the subsatellite. At the Shuttle, the tether attachment is made at the end of a boom deployed out of the payload bay. This attachment noticeably affects retrieval dynamics of the satellite pendulous motion. At the satellite, the tether attachment is assumed to be made on the circumference of the satellite. This attachment greatly affects the attitude motion of the satellite about its own center-of-mass. Computer simulation results are presented showing the effects of the Shuttle boom in a three-dimensional model and the effects of satellite attachment in a planar model.

Gresham, L. L.↗