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The paper presents a detailed parameterization of the transverse momentum in hadronic collisions on multiplicity and on beam momentum. Hadronic collisions are considered at energies below the ultra-high energy domain, on the basis of an uncertainty relation and a naive eikonal model with an impact-parameter-dependent multiplicity.
A cosmic ray mass spectrometer using a superconducting magnet, digitized wire spark chambers, and a scintillation counter time of flight system, has been operated at an altitude of 2750 meters. The apparatus is most sensitive to charged particles with momentum to mass ratios between 0.2 and 2.0. Results for the momentum spectra of protons and deuterons are presented, as well as upper limits for H-3 and He-3. The reaction nucleon + nucleon yields deuteron + pion accounts for part of the observed deuteron spectrum in the 0.9 to 3 GeV/c region.-
Floating reference frames were investigated in order to allow first order vibration analysis in the presence of large system rotations. When the deformations of an elastic continuum are expanded in terms of the free-free modes of an unconstrained system, the rigid body modes are found to be fixed relative to the Tisserand frame, with respect to which the relative momentum is zero. The proof presented for this is based on the orthogonality condition for modes with distinct natural frequencies. This result also guarantees the independence of coordinates for all modes with nonzero natural frequencies. A Modified Tisserand Constraint is introduced in order to define a floating reference frame with similar properties for an elastic body which contains a spinning rotor. Finite element equations of motion are derived for a completely flexible spacecraft with momentum exchange controllers, using a Modified Tisserand Frame. The deformable systems covered in this application are assumed to undergo only small rotations, and therefore the rotor torques must formally be small, although in engineering applications it may be possible to relax this constraint. A modal analysis is performed for the system and the resulting set of equations is reduced in number by a truncation procedure for more efficient system simulation.
This paper considers the application of an Annular Momentum Control Device (AMCD) to both fine pointing and large-angle maneuvering of a large space telescope (LST). The AMCD, which consists principally of a spinning rim suspended in noncontacting electromagnetic bearings, represents a new development in momentum storage devices. A nonlinear mathematical model of the AMCD/LST system is derived. An optimal stochastic fine-pointing controller is designed via LQG theory and the minimum-energy maneuvering problem is solved via a gradient technique. Number of state variable and control variable constraints, as well as all trigonometric nonlinearities, are considered in the latter part.
An experimental study was conducted using a plate test bed having a turbulent boundary layer to determine the momentum transfer to the faces of step/cavity combinations on the plate. Experimental data were obtained from configurations including an isolated configuration and an array of blocks in tile patterns. A momentum transfer correlation model of pressure forces on an isolated step/cavity was developed with experimental results to relate flow and geometry parameters. Results of the experiments reveal that isolated step/cavity excrecences do not have a unique and unifying parameter group due in part to cavity depth effects and in part to width parameter scale effects. Drag predictions for tile patterns by a kinetic pressure empirical method predict experimental results well. Trends were not, however, predicted by a method of variable roughness density phenomenology.
This paper discusses the application of an Annular Momentum Control Device (AMCD) to fine pointing control of a large space telescope (LST). The AMCD represents a new development in the field of momentum storage devices. A linearized mathematical model is developed for the AMCD/LST system, including the magnetic suspension actuators. Two approaches to control system design are considered. The first approach uses a stochastic linear-quadratic Gaussian controller which utilizes feedback of all states. The second approach considers a more practical control system design in which the axial and radial loops are designed independently.
We consider how an axisymmetric, uniformly and slowly rotating homogeneous star might be affected by the loss of energy and angular momentum via neutrino emission. For example, these losses can cause a collapsing, rotating star to flatten either faster or slower than would be the case if these losses were not taken fully into account, depending on the efficiency of the angular momentum loss mechanism.
Perturbations in the structure of the neutral atmosphere were measured in narrow latitude bands near the dayside polar cusp by mass spectrometers aboard the S3-1 and Esro 4 satellites. The disturbances are characterized by an in-phase variation of both the lighter and the heavier species. They are observed to occur in latitude bands of about 5-10 deg extent in the altitude region of 200 km during periods of increased geomagnetic activity. It is suggested that thermospheric winds driven by momentum sources associated with ion convection are the predominant cause for these disturbances. The narrow structure features associated with the momentum source are superimposed on the thermospheric changes caused by Joule heating. Both effects may be present simultaneously, resulting in a complex response pattern of the neutral gas composition in the thermosphere.
The observed surface angular velocity of main-sequence stars shows a sharp decrease at about spectral type F6. It is suggested that stars more massive than F6 cannot experience an appreciable angular-momentum loss because their convection zones cannot sustain a magnetic dynamo: without a magnetic field the angular-momentum loss is very small. The influence of rotation on the convective motions is essential for the existence of a solar-type dynamo. Rotation can influence these convective motions only if the typical convective time is larger than the rotation time. For main-sequence stars of different masses and chemical compositions the dimensionless parameter (convective velocity/sum's angular velocity times mixing length in the lower part of the convection zone) is evaluated. It is shown that this parameter increases very sharply for stars whose mass exceeds that defined by the relation log(star mass/solar mass) is of the order of 0.1. Thus even for large angular velocities, magnetic dynamos are not feasible if log(star mass/solar mass) appreciably exceeds 0.1.
Magnetic bearings used for the suspension of momentum wheels provide conclusive advantages: the low friction torques and the absence of abrasion allow the realization of lightweight high speed wheels with high angular momentum and energy storage capacity and virtually unlimited lifetime. The use of actively controlled bearings provides a magnetic gimballing capability by applying the external signals to the two servo loops controlling the rotational degrees of freedom. Thus, an attitude control system can be realized by using only one rotating mass for 3-axis active satellite stabilization.
The dual-momentum control device being studied for large spacecraft consists of two counter-rotating rings, each designated as an annular momentum control device (AMCD). For large rings, flexibility is appreciable and it becomes necessary to account for the distributed nature of the rings in the design of the magnetic bearing controllers. Also, ring behavior is unpredictably sensitive to ring temperature, spin rate, manufacturing imperfections, and other variables. For that reason, an adaptive control system is being sought for ring stabilization and maneuvering. This paper details an original adaptive control methodology for distributed parameter systems and illustrates this technique by application to AMCD stabilization.
Feasibility of the annular momentum control device (AMCD) for the control and stabilization of spacecraft is presented. The AMCD is momentum storage equipment consisting of a thin rim, magnetically suspended and rotated by noncontacting electromagnetic actuators. The laboratory model AMCD, the rim, and the magnetic suspension system are described, along with their evaluation tests. Because it utilizes permanent magnet flux biased magnetic bearing elements, the original laboratory model magnetic suspension system produced control limitations, and a new suspension system which used zero flux bias was designed and fabricated. Tests of the improved system show that a medium control loop bandwidth is required to achieve stability at low rim velocities, but at higher rim speed the bandwidth of the control loop interacts with bending modes of the rim and causes instability. Decreasing the bandwidth by changing to a precession control mode is discussed, and the results of such a computer simulation are presented.
An approximation to a previously presented rigorous description of molecular (atom-atom) collisions occurring in the presence of intense radiation is investigated. This rigorous description explicitly considers the angular momentum transferred between the molecule and the radiation field in the absorption or emission of a photon, but involves a complicated system of close-coupled equations which must be solved independently for each projection M of the initial, total molecular angular momentum. (This is a direct consequence of the lack of rotational invariance in the molecule-field problem). These equations are solved for a model system which mimics the collision of a halogen with a rare gas atom. Empirical observations made in the course of performing these calculations lead to the development of an approximation which avoids the repeated calculations for each initial M. This orientational average approximation greatly reduces the effort required to describe the system, and for the model calculation, yields accurate results for field intensities as high as 10 GW/sq cm.
A description of a digital computer simulation of an Annular Momentum Control Device (AMCD) laboratory model is presented. The AMCD is a momentum exchange device which is under development as an advanced control effector for spacecraft attitude control systems. The digital computer simulation of this device incorporates the following models: six degree of freedom rigid body dynamics; rim warp; controller dynamics; nonlinear distributed element axial bearings; as well as power driver and power supply current limits. An annotated FORTRAN IV source code listing of the computer program is included.
The development model for an optical scanning mechanism assembly is described as being two equal inertial masses which collide with each other to minimize the momentum transfer to the satellite and other mounted instruments. The design criteria for the mirror, the compensating inertia structure and other components are given. The details of the design are discussed and related test results are presented, which show the validity of the design concept for momentum compensation.
Analytical formulas are derived for orbit-averaged behavior of magnetic control laws for unloading the excess angular momentum of a spacecraft reaction wheel control system in the presence of secular environmental torques. The specific example of an axially symmetric spacecraft with an inertially fixed attitude for which the dominant environmental torque is the gravity-gradient torque is treated in detail, but extensions of the general approach to other inertially fixed and earth-pointing spacecraft are discussed. The analytical formulas are compared to detailed simulations performed for the Solar Maximum Mission spacecraft, and agreement to within 10% is found. The analytical formulas can be used in place of detailed simulations for preliminary studies, and can be used to find selected cases giving the most stringent tests of momentum unloading capability for which detailed simulations may be performed.
For application to aeronomy and space physics problems involving strongly magnetized plasma flows, we derived momentum and energy exchange collision terms for interpenetrating bi-Maxwellian gases. Collision terms were derived for Coulomb, Maxwell molecule, and constant collision cross-section interaction potentials. The collision terms are valid for arbitrary flow velocity differences and temperature differences between the interacting gases as well as for arbitrary temperature anisotropies. The collision terms had to be evaluated numerically and the appropriate coefficients are presented in tables. However, the collision terms were also fitted with simplified expressions, the accuracy of which depends on both the interaction potential and the temperature anisotropy. In addition, we derived the closed set of transport equations that are associated with the momentum and energy collision terms.
This paper addresses the dynamic characteristics of a momentum biased spacecraft (Magsat) which was placed in an elliptic, sun synchronous, low earth orbit. It discusses various dynamic phenomena observed, develops models for their plausible explanation, and suggests techniques for preventing or minimizing adverse phenomena. An aerodynamic coefficient model which accounts for atmospheric superrotation is proposed. This model is used to conduct analysis and simulations, the results of which are shown to be compatible with data taken by Magsat. A control philosophy is developed, and analytic expressions for the long term motion of the momentum biased axis for special cases are derived.