Satellite dynamics under the influence of gravitational and aerodynamic torques. A study of stability of equilibrium positions

The dynamics of the rotational motion of a satellite, moving in the central Newtonian force field under the influence of gravitational and aerodynamic torques, is investigated. The paper proposes a method for determining all equilibrium positions (equilibrium orientations) of a satellite in the orbital coordinate system for specified values of aerodynamic torque and the major central moments of inertia; the sufficient conditions for their existence are obtained. For each equilibrium orientation the sufficient stability conditions are obtained using the generalized energy integral as the Lyapunov function. The detailed numerical analysis of the regions where the stability conditions of the equilibrium positions are satisfied is carried out depending on four dimensionless parameters of the problem. It is shown that, in the general case, the number of satellite’s equilibrium positions, for which the sufficient stability conditions are satisfied, varies from 4 to 2 with an increase in the value of the aerodynamic torque magnitude.     

Composition of solar cosmic rays

Summary The general features of the solar particle composition now seem to be clear. The two most abundant components, protons and helium nuclei, have different velocity spectra, similar, but not exactly identical rigidity spectra, and varying relative abundances. The multiply charged nuclei, on the other hand, appear to have the same spectral shape and relative abundances each time measurements are made, at least in the region from 42 to 135 MeV/nucleon. Further, these relative abundances seem to reflect those of the solar atmosphere insofar as comparison can be made. Electrons are rare, but high energy electrons are not expected to be plentiful due to the probable high rate of energy loss caused by synchrotron radiation at the sun. Energetic neutrons were also not expected in large quantity and have not been observed. Finally, there is positive evidence that very small quantities of deuterons exist, probably in an amount which is about 10^-3 or less of the proton abundance.The experimental data indicate that the propagation phenomenon is not purely rigidity dependent. Although the propagation of solar particles is still not well understood, the development of theories which take into account both the general magnetic field and the inhomogeneities in the field seem to hold some promise of explaining the experimental results. The composition data have also established important restraints which any acceleration theory must satisfy, and thereby contributed greatly to the very difficult problem of determining the acceleration mechanism.The similarity of the relative abundance of the energetic solar particles and the nuclei in the sun's photosphere suggested the possibility of having a new means of estimating the solar neon and helium abundances. This very interesting possibility will have to be explored by further testing of the composition of future solar particle events. Finally, it was seen that the composition was a very strong argument against most stars being the principal source of high energy non-solar cosmic rays, and, therefore, special sources, such as supernovae or possibly quasistellar objects, should be considered as much more likely prospects for the origin of cosmic rays.The results which have been obtained thus far on the composition of solar cosmic rays have indicated that further research in this area of study should be very rewarding and of value to many fields of physics. Further data on the composition and relative, as well as absolute, energy spectra of the various components are needed throughout many events. More experiments also should be performed to determine the properties of the rare components, deuterons, tritons, He³ nuclei, electrons, neutrons, and the heavier nuclei. When these experiments are complete, the knowledge which is needed to aid in answering the solar and astrophysical problems discussed in this review should be at hand.     

Laboratory experiments of magnetospheric interest

Space-related laboratory experiments can play an important role as a complement to observations and active experiments in the magnetosphere. Excluding laboratory experiments for mere developing or testing of techniques for space experiments, we may distinguish between two major types: (1) partial scale model experiments and (2) experiments for clarifying basic plasma physical processes known or expected to be important in the magnetosphere (but without the ambition to simulate actual space configurations). The limitations and potentialities of both types are discussed and examples of experiments are given. It is concluded that there should be an increasing need for the experiments of the second type. In particular, they are needed for the clarification of the response of a thin plasma to electric fields and its ability to carry electric currents. This encompasses such key questions as the nature and role of anomalous resistivity (and electron runaway in its presence), the possible formation of double layers (and the acceleration processes associated with them) and rapid dissipation of magnetic-field energy.     

Transformation of the Spectrum of a Signal in Communication between Relativistically Moving Inertial Frames

Future space exploration may involve communications between spacecraft moving at relativistic velocities. One of the significant problems associated with such communication is spectral distortion of signals which are propagated between relativistic frames. This distortion is generated by both changing propagation distances and purely relativistic electromagnetic field transformations. In this paper a linear integral transformation is formulated for relating the Fourier spectra of the source antenna excitation current and the resulting incident electric field at the receiving antenna. The kernel of the transformation is evaluated for the case of a steerable source antenna tracking on the advanced receiver position. The transformation is then applied to the case of an ideal thin-wire half-wave dipole source antenna excited by a narrowband, double-sideband modulated current. The specific distortions of spectral spreading and translation are then related to increased bandwidth and upper cutoff frequency requirements of receiving systems in relativistic applications.     

Identification of Aircraft Stability and Control Parameters Using Hierarchical State Estimation

Previous attempts to identify aircraft stability and control derivatives from flight test data, using three-degrees-of-freedom (3-DOF) longitudinal or lateral-directional perturbation equation-of-motion models, suffer from the disadvantage that the coupling between the longitudinal and lateral-directional dynamics has been ignored. In this paper, the identification of aircraft stability parameters is accomplished using a more accurate 6-DOF model which includes this coupling. Hierarchical system identification theory is used to reduce the computational effort involved. The 6-DOF system of equations is first decomposed into two 3-DOF subsystems, one for the longitudinal dynamics and the other for the lateral-directional dynamics. The two subsystem parameter identification processes are then coordinated in such a way that the overall system parameter identification problem is solved. Next, a six-subsystem decomposition is considered. Computational considerations and comparison with the unhierarchically structured problem are presented.     

Linear FM Signal Formats for Beacon and Communication Systems

This paper examines the capabilities of the class of linear FM spread-spectrum signals within the context of potential communications systems usage in order to establish some performance criteria and bounds that permit comparison with other spread-spectrum formats. A systematic basis is provided for parameter selection for this class of signals by examining the interaction a mong the frequency-modulation indices, time-bandwidth product, and cross-talk criteria that determine the number of effective linear FM signals (or channels) that can be used within the constraints of a bounded time-frequency region. A general expression is derived relating N, the number of useful signals, R2, a cross-talk parameter, ToWo, the mean time-bandwidth product, and ?max and ?min, the maximum and minimum FM rates of the signal set. Canonic signal processor structures are described for ensembles of linear FM signals that have either constant duration or constant bandwidth. It is then shown that the signal modulation format can be modified in accordance with classical paired-echo theory to expand the utility of this class of signals in both synchronous and nonsynchronous operations to yield the equivalent of time-division and code multiplexing. Possible applications for this signal format are discussed.