Behavior of nearby synchronous rotations of a Poincaré–Hough satellite at low eccentricity (original) (raw)

Rotation of Synchronous Satellites Application to the Galilean Satellites

Celestial Mechanics & Dynamical Astronomy, 2004

An analytical theory of the rotation of a synchronous satellite is developed for the application to the rotation of the Galilean satellites. The theory is developed in the framework of Hamiltonian mechanics, using Andoyer variables. Special attention is given to the frequencies of libration as functions of the moments of inertia of the satellite.

Synchronous Locking of Tidally Evolving Satellites

Icarus, 1996

In general, consider a planetary satellite (see Fig. 1) whose circular orbit normal K is inclined by an inclination Satellite spin states evolve under the action of solid body torques and tidal forces. The tidal effects result in a damping i with respect to an invariable plane normal n , about which of fast spin rates and, ultimately, in the locking of the spin it precesses with a rate ϪȐ (in rad/year). For close planeinto what are known as Cassini states. The dynamical equations tary satellites, the invariable plane is the planet's equatorial for the satellite spin vector are derived, non-dimensionalized, plane, and the orbit precession is caused by the oblateness and discussed. The non-dimensional parameters that determine of the planet. In general, the invariable plane is the satelthe ultimate fate of the system are identified. A review of Cassini lite's Laplace plane in the three body system (Goldreich states is given, and then the effect of a permanent triaxial 1966a, Ward 1981). The satellite's spin angular momentum deformation on the evolution of the spin vector is explored. in the k direction is tilted by an obliquity with respect We find that for the parameter ranges of most real Solar System to its orbit-plane normal K. If the satellite is oblate, the satellites which have been despun to synchronous rotation, planet exerts a torque which attempts to cause a precession occupation of Cassini state 1 is the only possible endpoint. The of the spin axis about K. We will assume in what follows existence of a non-axially symmetric deformation destabilizes the higher obliquity Cassini state 2. We discuss the possibility that the satellite is in principal-axis rotation about its axis of tumbling occurring during the spin-down and argue that of maximum moment of inertia. Averaged around the satthis does not effect our basic conclusions. The non-occupancy ellite's orbit, this torque is given by ϪSC cos sin , where of Cassini state 2 (except for the Moon, for which state 1 C is the satellite's moment of inertia about the spin axis and does not exist) is not a function of initial conditions or spin configuration occupied at synchronous lock, as previously hypothesized.

Solutions of the motion of synchronous satellites with arbitrary eccentricity and inclination

Flight Mechanics Estimation Theory Symposium, 1975

A fmt-order, semianalytical theory for the long-term motion of resonant satellites is presented. The theory is valid for all eccentricities and inclinations and for all commensurability ratios. The method allows the inclusion of all the zonal 2nd tesserd harmonics as well as lunisolar perturbations and radiation pressure. The method is applied to a synchronous satellite including only the J, and J, harmonics. Global, long-term solutions for this problem, eccentricity, argument of perigee, and inclination are obtained.

The rotation of Io predicted by Poincaré-Hough model

2012

This note tackles the problem of the rotation of Io with the 4-degrees of freedom Poincaré-Hough model. Io is modeled as a 2-layer body, i.e. a triaxial fluid core and a rigid outer layer. We show that the longitudinal librations should have an amplitude of about 30 arcseconds, independent of the composition of the core. We also estimate the tidal instability of the core, and show that should be slowly unstable.

The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2 : 1 Resonance

Mathematical Problems in Engineering, 2012

The orbital dynamics of synchronous satellites is studied. The 2 : 1 resonance is considered; in other words, the satellite completes two revolutions while the Earth completes one. In the development of the geopotential, the zonal harmonicsJ20andJ40and the tesseral harmonicsJ22andJ42are considered. The order of the dynamical system is reduced through successive Mathieu transformations, and the final system is solved by numerical integration. The Lyapunov exponents are used as tool to analyze the chaotic orbits.

Sixth International Symposium on Classical and Celestial Mechanics (CCMECH6)

2007

In this work we consider a 1:-1 non semi-simple resonant periodic orbit of a three-degrees of freedom real analytic Hamiltonian system. From the formal analysis of the normal form, it is proved the branching off a two-parameter family of two-dimensional invariant tori of the normalised system, whose normal behaviour depends intrinsically on the coefficients of its low-order terms. Thus, only elliptic or elliptic together with parabolic and hyperbolic tori may detach form the resonant periodic orbit. Both patterns are mentioned in the literature as the direct and, respectively, inverse quasiperiodic Hopf bifurcation. In this report we focus on the direct case, which has many applications in several fields of science. Thus, we present here a summary of the results, obtained in the framework of KAM theory, concerning the persistence of most of the (normally) elliptic tori of the normal form, when the whole Hamiltonian is taken into account, and to give a very precise characterisation o...

Bifurcation and Chaos in an Apparent-Type Gyrostat Satellite

Nonlinear Dynamics, 2005

Attitude dynamics of an asymmetrical apparent gyrostat satellite has been considered. Hamiltonian approach and Routhian are used to prove that the dynamics of the system consists of two separate parts, an integrable and a non-integrable. The integrable part shows torque free motion of gyrostat, while the non-integrable part shows the effect of rotation about the earth and asphericity of the satellite's inertia ellipsoid. Using these results, theoretically when the non-integrable part is eliminated, we are able to design a satellite with exactly regular motion. But from the engineering point of view the remaining errors of manufacturing process of the mechanical parts cause that the non-integrable part can not be eliminated, completely. So this case can not be achieved practically. Using Serret-Andoyer canonical variable the Hamiltonian transformed to a more appropriate form. In this new form the effect of the gravity, asphericity, rotational motion and spin of the rotor are explicitly distinguished. The results lead us to another way of control of chaos. To suppress the chaotic zones in the phase space, higher rotational kinetic energy can be used. Increasing the parameter related to the spin of the rotor causes the system's phase space to pass through a heteroclinic bifurcation process and for the sufficiently large magnitude of the parameter the heteroclinic structure can be eliminated. Local bifurcation of the phase space of the integrable part and global heteroclinic bifurcation of whole system's phase space are presented. The results are examined by the second order Poincaré surface of section method as a qualitative, and the Lyapunov characteristic exponents as a quantitative criterion.

Dynamics around non-spherical symmetric bodies – I. The case of a spherical body with mass anomaly

Monthly Notices of the Royal Astronomical Society, 2021

The space missions designed to visit small bodies of the Solar system boosted the study of the dynamics around non-spherical bodies. In this vein, we study the dynamics around a class of objects classified by us as non-spherical symmetric bodies, including contact binaries, triaxial ellipsoids, and spherical bodies with a mass anomaly, among others. In this work, we address the results for a body with a mass anomaly. We apply the pendulum model to obtain the width of the spin–orbit resonances raised by non-asymmetric gravitational terms of the central object. The Poincaré surface of section technique is adopted to confront our analytical results and to study the system’s dynamics by varying the parameters of the central object. We verify the existence of two distinct regions around an object with a mass anomaly: a chaotic inner region that extends beyond the corotation radius and a stable outer region. In the latter, we identify structures remarkably similar to those of the classica...

Dynamics of tidal synchronization and orbit circularization of celestial bodies

Physical review. E, Statistical, nonlinear, and soft matter physics, 2008

We take a dynamical-systems approach to study the qualitative dynamical aspects of the tidal locking of the rotation of secondary celestial bodies with their orbital motion around the primary. We introduce a minimal model including the essential features of gravitationally induced elastic deformation and tidal dissipation that demonstrates the details of the energy transfer between the orbital and rotovibrational degrees of freedom. Despite its simplicity, our model can account for both synchronization into the 1:1 spin-orbit resonance and the circularization of the orbit as the only true asymptotic attractors, together with the existence of relatively long-lived metastable orbits with the secondary in p : q synchronous rotation.

Periodic solutions for rotational motion of an axially symmetric charged satellite

Applied Mathematical Sciences, 2015

The present paper is devoted to the investigation of sufficient conditions for the existence of periodic solutions in the vicinity of stationary motion of a charged satellite in elliptic orbit. Lorentz forces which result from the motion of a charged satellite relative to the magnetic field of the Earth are considered. An axial symmetry is assumed about the center of mass of the satellite. In addition to the Lorentz force the perturbation caused by gravitational and magnetic fields of the Earth are considered. The stationary solutions and periodic orbits close to them are obtained using the Lyapunov theorem of holomorphic integral. Numerical results are used to explain the periodic motion of a certain satellite. It is shown that the charge-to-mass ratio has a significant influence on the periodic motion of satellites.