A note on the periodic orbits of a self excited rigid body

The aim of the present paper is to study the periodic orbits of a perturbed self excited rigid body with a fixed point. For studying these periodic orbits we shall use averaging theory of first order.

Invariability, orbits and fuzzy attractors

In this paper, we present a generalization of a new systemic approach to abstract fuzzy systems. Using a fuzzy relations structure will retain the information provided by degrees of membership. In addition, to better suit the situation to be modelled, it is advisable to use T-norm or T-conorm distinct from the minimum and maximum, respectively. This gain in generality is due to the completeness of the work on a higher level of abstraction. You cannot always reproduce the results obtained previously, and also sometimes different definitions with different views are obtained. In any case this approach proves to be much more effective when modelling reality.

Orbits of the double stars, A B of [Epsilon] Hydrae and ? 883, by the graphical method.

Type-written ms.

Tables for rocket and comet orbits /

Bibliography: p. xxiii.

Particle orbits in the static sheet pinch /

"April 1963."

On the orbits described by bodies revolving in given planes round immoveable centres of forces.

Preface signed: W. Wilkinson.

Intermediary equatorial orbits of an artificial satellite,

"NBS project 1104-12-11440."

Various techniques and procedures for refining ERS-1 orbits

The satellite ERS-1 was launched in July 1991 in a period of high solar activity. Sparse laser tracking and the failure of the experimental microwave system (PRARE) compounded the orbital errors which resulted from mismodelling of atmospheric density and hence surface forces. Three attempts are presented here to try and refine the coarse laser orbits of ERS-1, made prior to the availability of the full altimetric dataset. The results of the first attempt indicate that by geometrically modelling the satellite shape some improvement in orbital precision may be made for any satellite; especially one where no area tables already exist. The second and third refinement attempts are based on the introduction of data from some second satellite; in these examples SPOT-2 and TOPEX/Poseidon are employed. With SPOT-2 the method makes use of the orbital similarities to produce along-track corrections for the more fully tracked SPOT-2. Transferring these corrections to ERS-1 produces improvements in the precise orbits thus determined. With TOPEX/Poseidon the greater altitude results in a more precise orbit (gravity field and atmospheric errors are of less importance). Thus, by computing height differences at crossover points of the TOPEX/Poseidon and ERS-1 ground tracks the poorer orbit of ERS-1 may be improved by the addition of derived radial corrections. In the positive light of all three results several potential modification are suggested and some further avenues of investigation indicated.

Drag coefficients with applications to satellite orbits

In the last twenty or so years the results of theory and experiment have produced much information on the characteristics of gas-surface interactions relevant to a satellite in hyperthermal free-molecular flow. This thesis contains reviews of the rarefied gas dynamics applicable to satellites and has attempted to compare existing models of gas-surface interaction with contemporary knowledge of such systems. It is shown that a more natural approach would be to characterise the gas-surface interaction using the normal and tangential momentum accommodation coefficients, igma' and igma respectively, specifically in the form igma = constant , igma' = igma'0 -igma'1sec i where i is the angle subtended between the incident flow and the surface normal and igma,igma'0 and igma'1 are constants. Adopting these relationships, the effects of atmospheric lift on inclination, i, and atmospheric drag on the semi-major axis, a, and eccentricity, e, have been investigated. Applications to ANS-1 (1974-70A) show that the observed perturbation in i can be ascribed primarily to non-zero igma'1 whilst perturbations in a and e produce constraint equations between the three parameters. The numerical results seem to imply that a good theoretical orbit is achieved despite a much lower drag coefficient than anticipated by earlier theories.

Application of ERS-1 and Topex/Poseidon altimetry using precise orbits

The work described in this thesis concerns the application of radar altimetry, collected from the ERS-1 and TOPEX/POSEIDON missions, to precise satellite orbits computed at Aston University. The data is analysed in a long arc fashion to determine range biases, time tag biases, sea surface topographies and to assess the radial accuracy of the generated orbits through crossover analysis. A sea surface variability study is carried out for the North Sea using repeat altimeter profiles from ERS-1 and TOPEX/POSEIDON in order to verify two local U.K. models for ocean tide and storm surge effects. An on-side technique over the English Channel is performed to compute the ERS-1, TOPEX and POSEIDON altimeter range biases by using a combination of altimetry, precise orbits determined by short arc methods, tide gauge data, GPS measurements, geoid, ocean tide and storm surge models. The remaining part of the thesis presents some techniques for the short arc correction of long arc orbits. Validation of this model is achieved by way of comparison with actual SEASAT short arcs. Simulations are performed for the ERS-1 microwave tracking system, PRARE, using the range data to determine time dependent orbit corrections. Finally, a brief chapter is devoted to the recovery of errors in station coordinates by the use of multiple short arcs.

On the Asymptotic Distribution of Closed Orbits for a Class of Open Billiards

2000 Mathematics Subject Classification: 37D40.

Orbits of semigroups of truncated convolution operators

We prove that a semigroup generated by finitely many truncated convolution operators on $L_p[0, 1]$ with 1 ≤ p < ∞ is non-supercyclic. On the other hand, there is a truncated convolution operator, which possesses irregular vectors.

On the rotation of co-orbital bodies in eccentric orbits

We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in the entire domain of horseshoe and tadpole orbit, for moderate eccentricities. We show that there are three different families of spin-orbit resonances, one depending on the eccentricity, one depending on the orbital libration frequency, and another depending on the pericenter's dynamics. We can estimate the width and the location of the different resonant islands in the phase space, predicting which are the more likely to capture the spin of the rotating body. In some regions of the phase space the resonant islands may overlap, giving rise to chaotic rotation.

Automatic classification of stellar orbits in axisymmetric potentials

Within the classification of orbits in axisymmetric stellar systems, we present a new algorithm able to automatically classify the orbits according to their nature. The algorithm involves the application of the correlation integral method to the surface of section of the orbit; fitting the cumulative distribution function built with the consequents in the surface of section of the orbit, we can obtain the value of its logarithmic slope m which is directly related to the orbit’s nature: for slopes m ≈ 1 we expect the orbit to be regular, for slopes m ≈ 2 we expect it to be chaotic. With this method we have a fast and reliable way to classify orbits and, furthermore, we provide an analytical expression of the probability that an orbit is regular or chaotic given the logarithmic slope m of its correlation integral. Although this method works statistically well, the underlying algorithm can fail in some cases, misclassifying individual orbits under some peculiar circumstances. The performance of the algorithm benefits from a rich sampling of the traces of the SoS, which can be obtained with long numerical integration of orbits. Finally we note that the algorithm does not differentiate between the subtypes of regular orbits: resonantly trapped and untrapped orbits. Such distinction would be a useful feature, which we leave for future work. Since the result of the analysis is a probability linked to a Gaussian distribution, for the very definition of distribution, some orbits even if they have a certain nature are classified as belonging to the opposite class and create the probabilistic tails of the distribution. So while the method produces fair statistical results, it lacks in absolute classification precision.

Physical and dynamical characterization of (5201) Ferraz-Mello, a possible extinct Jupiter family comet

Context. The subject of asteroids in cometary orbits (ACOs) has been of growing interest lately. These objects have the orbital characteristics typical of comets, but are asteroidal in appearance, i.e., show no signs of a coma at any part of their orbits. At least a fraction of these objects are thought to be comets that have either exhausted all their volatile content or developed a refractory crust that prevents sublimation. In particular, the asteroid ( 5201) Ferraz-Mello has, since its discovery, been suspected to be an extinct Jupiter family comet due to the peculiar nature of its orbit. Aims. The aim of this work is to put constraints on the possible origin of ( 5201) Ferraz-Mello by means of spectroscopic characterization and a study of the dynamics of this asteroid. Methods. We used the SOAR Optical Imager (SOI) to obtain observations of ( 5201) Ferraz-Mello using four SDSS filters. These observations were compared to asteroids listed in the Sloan Moving objects catalog and also to photometry of cometary nuclei, Centaurs, and TNOs. The orbital evolution of ( 5201) Ferraz-Mello and of a sample of asteroids and comets that are close to that object in the a - e plane were simulated using a pure N-body code for 4 000 years forward and 4 000 years backward in time. Results. The reflectance spectrum obtained from its colors in the SDSS system is unusual, with a steep spectral gradient that is comparable to TNOs and Centaurs, but with an increase in the reflectance in the g band that is not common in those populations. A similar behavior is seen in cometary nuclei that were observed in the presence of a faint dust coma. The dynamical results confirm the very chaotic evolution found previously and its dynamical similarity to the chaotic evolution of some comets. The asteroid is situated in the very stochastic layer at the border of the 2/1 resonance, and it has a very short Lyapunov time ( 30 - 40) years. Together, the spectral characteristcs and the dynamical evolution suggest that ( 5201) Ferraz-Mello is a dormant or extinct comet.