Quaternion regularization in celestial mechanics and astrodynamics and trajectory motion control. I

Regularization problems in celestial mechanics and astrodynamics are considered. The fundamental regular quaternion models of celestial mechanics and astrodynamics are presented. It is shown that the efficiency of analytical investigation and numerical solution of boundary problems of optimal trajectory motion control of spacecraft may be increased using quaternion astrodynamics models. The regularization problem of celestial mechanics and astrodynamics that implies eliminating the feature, which arises in the equations of the two-body problem in case of impact of the second body with the central body, is considered in the first section of the paper. The quaternion method for regularizing the equations of the perturbed spatial two-body problem suggested by the author is presented; the method is compared with Kustaanheimo-Stiefel (KS) regularization. Demonstrative geometric and kinematic interpretations of regularizing transformations are provided. Regular quaternion equations for the two-body problem, which generalize the regular Kustaanheimo-Stiefel equations, as well as regular equations in quaternion osculating elements and quaternion regular equations for perturbed central motion of a material point, are considered. The papers on quaternion regularization in celestial mechanics and astrodynamics are briefly analyzed.     

Identification of a 2D turbulent wind spectrum

Turbulent wind spectrum models usually involve nonrational terms. For such models the development of a Markovian time simulator relies on a rational approximation obtained by the way of an identification stage. This paper presents a general method to manage this identification stage, that provides us with a family of stable rational approximations which is proved to converge towards the true model as the dimension increases. We first give an exact but infinite dimensional state space representation of the spectrum. It is based on the use of a diffusive equation. For bi-dimensional (2D) signals it also uses decoupling by spatial Fourier transformation. Then the discretization of this exact model leads easily to stable finite dimensional approximations over a prescribed frequency range. This approach is applied to the identification of a theoretical 2D turbulent wind spectrum, and of a 1D turbulent wind spectrum estimated from in flight recorded data.     

Sharp boundaries of solar wind plasma structures and their relationship to solar wind turbulence

Sharp (<10 min) and large (>20%) solar wind ion flux changes are common phenomena in turbulent solar wind plasma. These changes are the boundaries of small- and middle-scale solar wind plasma structures which can have a significant influence on Earth’s magnetosphere. These solar wind ion flux changes are typically accompanied by only a small change in the bulk solar wind velocity, hence, the flux changes are driven mainly by plasma density variations. We show that these events occur more frequently in high-density solar wind. A characteristic of solar wind turbulence, intermittency, is determined for time periods with and without these flux changes. The probability distribution functions (PDF) of solar wind ion flux variations for different time scales are calculated for each of these periods and compared. For large time scales, the PDFs are Gaussian for both data sets. For small time scales, the PDFs from both data set are more flat than Gaussian, but the degree of flatness is much larger for the data near the sharp flux change boundaries.     

ESA's Biopan 1--"Vitamin" experiment preliminary results

The purpose of “Vitamin” experiment is to study the efficiency of protective substances on three biological acellular systems aqueous solutions exposed to cosmic radiation in space. The first system “LDL”is a low density lipoprotein. The second is “E2-TeBG complexe” in which estradiol (E2) is bound to its plasmatic carrier protein, testosterone-estradiol binding globulin (TeBG). The third is “pBR 322”, a plasmid. “Vitamin” experiment was accomodated in the Biopan which had been mounted on the outer surface of a Foton retrievable satellite. The experiment was exposed to space environment during 15 days. A stable temperature of about 20 °C was maintained throughout the flight. “Vitamin” experiment preliminary results are presented and discussed.     

Cosmic ray studies at Moussala – Past,present and future

We review the main activities carried out at Moussala peak (2925 m above sea level, 42°11′N, 23°35′E) station in Bulgaria, connected with cosmic ray investigations during the last five decades. Several important results obtained at the station are reported. The detector design and corresponding methodological studies of the presently operational devices are shown as well, precisely the Cherenkov light telescope, lead free neutron monitor and muon telescope. The scientific potential of the existing complex is discussed.     

The Far Ultra-Violet Imager on the Icon Mission

ICON Far UltraViolet (FUV) imager contributes to the ICON science objectives by providing remote sensing measurements of the daytime and nighttime atmosphere/ionosphere. During sunlit atmospheric conditions, ICON FUV images the limb altitude profile in the shortwave (SW) band at 135.6 nm and the longwave (LW) band at 157 nm perpendicular to the satellite motion to retrieve the atmospheric O/N₂ ratio. In conditions of atmospheric darkness, ICON FUV measures the 135.6 nm recombination emission of \(\mathrm{O}^{+}\) ions used to compute the nighttime ionospheric altitude distribution. ICON Far UltraViolet (FUV) imager is a Czerny–Turner design Spectrographic Imager with two exit slits and corresponding back imager cameras that produce two independent images in separate wavelength bands on two detectors. All observations will be processed as limb altitude profiles. In addition, the ionospheric 135.6 nm data will be processed as longitude and latitude spatial maps to obtain images of ion distributions around regions of equatorial spread F. The ICON FUV optic axis is pointed 20 degrees below local horizontal and has a steering mirror that allows the field of view to be steered up to 30 degrees forward and aft, to keep the local magnetic meridian in the field of view. The detectors are micro channel plate (MCP) intensified FUV tubes with the phosphor fiber-optically coupled to Charge Coupled Devices (CCDs). The dual stack MCP-s amplify the photoelectron signals to overcome the CCD noise and the rapidly scanned frames are co-added to digitally create 12-second integrated images. Digital on-board signal processing is used to compensate for geometric distortion and satellite motion and to achieve data compression. The instrument was originally aligned in visible light by using a special grating and visible cameras. Final alignment, functional and environmental testing and calibration were performed in a large vacuum chamber with a UV source. The test and calibration program showed that ICON FUV meets its design requirements and is ready to be launched on the ICON spacecraft.     

Thermally excited vibrations of aircraft structural elements

This paper considers the axisymmetric transverse vibrations of aircraft nonuniform structural elements that are introduced by a thermal shock. Analytical solutions have been obtained and their numerical analysis has been performed.     

Cosmology and GUTs: The matter of the universe

To illustrate the interaction of Grand Unified Theories (GUTs), supersymmetry (SUSY), and cosmology, a worked example is carried out. This example is the dark matter problem, or “What is the dominant matter of the Universe?” It is shown that if GUTs are assumed then the primordial perturbations are probably adiabatic, if inflation is assumed then Ω = 1 and GUTs first name is probably SUSY. If Ω = 1, big bang nucleosynthesis tells us that the bulk of the matter is non-baryonic. SUSY-GUTs gives us some possible candidate inos to which massive neutrinos, axion or planetary mass black holes can be added. These candidates can be classified hot (or warm) or cold types of dark matter. It is shown that hot gives Ω = 1 and naturally gives large scale structure but does not give small scale structure or galaxy formation times, whereas cold gives small scale structure and formation times but cannot easily yield Ω = 1. It is concluded that either a hybrid of both hot and cold or non-random phases for the perturbations may be needed.