Reactive torques, due to anisotropic sublimation on a comet nucleus surface, produce slow variati... more 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 format... more 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 re... more 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 dynamic... more 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 ... more 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.
Reactive torques, due to anisotropic sublimation on a comet nucleus surface, produce slow variati... more 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 format... more 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 re... more 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 dynamic... more 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 ... more 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.
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