V. Sidorenko

Reactive torques, due to anisotropic sublimation on a comet nucleus surface, produce slow variations of its rotation. In this paper the secular effects of this sublimation are studied. The general rotational equations of motion are averaged over unperturbed fast rotation around the mass center (Euler-Poinsot motion) and over the orbital comet motion. We discuss the parameters that define typical properties of the rotational evolution and discover different classifications of the rotational evolution. As an example we discuss some possible scenarios of rotational evolution for the nuclei of the comets Halley and Borrelly.

This note presents a novel approach to maintain three-dimensional multi-tethered satellite formation in space. For a formation consisting of a main body connected by tethers with several deputy satellites (the so-called "hub-and-spoke" configuration) we demonstrate that under proper choice of the system's parameters the deputy satellites can move along Lissajous curves in the plane normal to the local vertical with all tethers stretched, the total force due to the tension forces acting on the main satellite is balanced in a way allowing it to be in relative equilibrium strictly below or strictly above the system's center of mass. We analyze relations between the system's essential parameters and obtain conditions under which the proposed motion does take place. We also study analytically the motion stability for different configurations and whether the deputy satellites can collide or the tethers can entangle. Our theoretical findings are corroborated and valid...

An analytical study is made of the asymptotic behavior of Lagrange gyroscope motions, close to regular precession, due to a small perturbation moment. An averaged system of equations of motion is obtained in terms of special evolution variables. The cases of a small constant moment and presence of a cavity filled by a high-viscosity fluid are considered in detail.

The rotational dynamics of outgassing cometary nuclei are investigated analytically using dynamical systems theory. We develop a general theory for the averaged evolution of a comet nucleus rotation state assuming that the nucleus is a spheroid (either prolate or oblate) and that the outgassing torques are a function of solar insolation and heliocentric distance. The resulting solutions are a function of the comet outgassing properties, its heliocentric orbit, and the assumed distribution of active regions on its surface. We find that the long-term evolution of the comet nucleus rotation is a strong function of the distribution of active regions over its surface. Specifically, we find that a comet nucleus with a uniformly active surface will tend towards a rotation state with a nutation angle of ~ 55 degrees and an angular momentum perpendicular to the sun-perihelion direction. Conversely, a comet nucleus with an isolated active region will tend towards a zero nutation angle with its symmetry axis and angular momentum aligned parallel to the sun-perihelion direction. For active surface regions between these extremes we find 4 qualitatively different dynamical outcomes. In all cases, the theory predicts that the comet nucleus angular momentum will have a secular increase, a phenomenon that could contribute to nucleus splitting of active comets. These results can be used to discriminate between competing theories of comet outgassing based on a nucelus' rotation state. They also allow for a range of plausible a priori constraints to be placed on a comet's rotation state to aid in the interpretation of its outgassing structure. This work was supported by the NASA JURRISS program under Grant NAG5-8715. AIN, AAV and VVS acknowledge support from Russian Foundation for Basic research via Grants 00-01-00538 and 00-01-0174 respectively. DJS acknowledges support from the PG&G program via Grant NAG5-9017.

The destruction of adiabatic invariants on resonances in multifrequency systems was investigated by A.I. Ncishtadt. He developed a general method which allows to derive the conditions for the existence of motions captured into resonance and to determine the moment of escape from the resonance if the moment of capture is known. Using this method we will study the resonance phenomena in the rotational motion of a slightly asymmetric magnetized satellite.

The investigations on long-term evolution of asteroid’s orbits are crucial to understanding the route through which the present configuration of the Solar system came to be. The so-called coorbiting asteroids (which share their orbits with major planets) attract the special attention in this connection: are they the primordial remnants of the building blocks of the corresponding major planet or are they the 'migrants' from the other parts of the Solar system? The most well known examples of co-orbits in natural objects are provided by Trojan groups of asteroids and by asteroids moving in horseshoe orbits. These asteroids are precluded from having relatively close encounters with their host planets. However, there exists another class of coorbiting objects in which the opposite is true: they remain very near to the host planet eternally or, at least, for long enough time. Since typically they never enter the planet’s Hill sphere, they cannot be considered as satellites in the...

We study the rotational motion of a rigid body carrying inextensible viscoelastic rods. We assume that the undeformed system admits the symmetry group of regular polyhedron. The rotational motion of this system is shown to be quite different from the Euler-Poinsot motion. The difference is due to the rod elasticity and to the high degree of system symmetry. We carry out a qualitative investigation of the evolution of rotations and single out possible stationary motions.

This chapter provides a short introduction into the main dynamical problems related to the rotational motion of celestial bodies. We start by considering various ways to characterize this motion and to derive the equations of motion. Although the main attention is given to the influence of the gravity torque on the rotational motion, the role of other torques is also briefly discussed. In an elementary way, we establish the key property of the non-resonant, slightly perturbed, rotational motion of a celestial body (under the action of gravity torque only) - the precession of the angular momentum vector around the normal to the orbital plane. The resonant spin-orbit coupling is considered as well.

Quasi-satellite orbits (QS-orbits) are studied in the framework of restricted spatial circular three-body problem. With the use of double numerical averaging evolutionary equations are constructed that describe the long-term behavior of asteroid's orbital elements. Special attention is paid to possible transitions between the motion in QS-orbit and in another types of orbits existing at 1:1 resonance. As an example of the motion in QS-orbit the dynamics of near-Earth asteroid 2004GU9 is considered.

The attitude motion of an artificial satellite carrying a strong magnet is studied. The approximate first integrals of the problem, i.e., adiabatic invariants, are indicated. The basic properties of the satellite motions close to the regular precessions with slowly varying parameters are established via the analysis of the adiabatic invariants.

The 3:1 mean-motion resonance of the planar elliptic restricted three body problem (Sun-Jupiter-asteroid) is considered. The double numeric averaging is used to obtain the evolutionary equations which describe the long-term behavior of the asteroid's argument of pericentre and eccentricity. The existence of the adiabatic chaos area in the system's phase space is shown.

The rotational dynamics of outgassing cometary nuclei are investigated analytically using dynamical systems theory. We develop a general theory for the averaged evolution of a comet nucleus rotation state assuming that the nucleus is a spheroid (either prolate or oblate) and that the outgassing torques are a function of solar insolation and heliocentric distance. The resulting solutions are a function of the comet outgassing properties, its heliocentric orbit, and the assumed distribution of active regions on its surface. We find that the long-term evolution of the comet nucleus rotation is a strong function of the distribution of active regions over its surface. Specifically, we find that a comet nucleus with a uniformly active surface will tend towards a rotation state with a nutation angle of ~ 55 degrees and an angular momentum perpendicular to the sun-perihelion direction. Conversely, a comet nucleus with an isolated active region will tend towards a zero nutation angle with its symmetry axis and angular momentum aligned parallel to the sun-perihelion direction. For active surface regions between these extremes we find 4 qualitatively different dynamical outcomes. In all cases, the theory predicts that the comet nucleus angular momentum will have a secular increase, a phenomenon that could contribute to nucleus splitting of active comets. These results can be used to discriminate between competing theories of comet outgassing based on a nucelus' rotation state. They also allow for a range of plausible a priori constraints to be placed on a comet's rotation state to aid in the interpretation of its outgassing structure. This work was supported by the NASA JURRISS program under Grant NAG5-8715. AIN, AAV and VVS acknowledge support from Russian Foundation for Basic research via Grants 00-01-00538 and 00-01-0174 respectively. DJS acknowledges support from the PG&G program via Grant NAG5-9017.