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

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Jarbas Cordeiro Sampaio ◽  
Rodolpho Vilhena de Moraes ◽  
Sandro da Silva Fernandes
Keyword(s):  
Dynamical System ◽  
Numerical Integration ◽  
Lyapunov Exponents ◽  
Orbital Dynamics ◽  
Zonal Harmonics ◽  
Chaotic Orbits ◽  
The Earth ◽  
Tesseral Harmonics ◽  
Final System

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.

PLANETARY SELF-ORGANIZATION

2020 ◽  
Vol 42 (3) ◽  
pp. 271-282
Author(s):  
OLEG IVANOV
Keyword(s):  
Dynamical System ◽  
Heat Source ◽  
Mantle Convection ◽  
Plate Tectonics ◽  
Rotation Speed ◽  
Self Organization ◽  
Heat Sources ◽  
Kinematic Parameters ◽  
The Earth ◽  
New Type

The general characteristics of planetary systems are described. Well-known heat sources of evolution are considered. A new type of heat source, variations of kinematic parameters in a dynamical system, is proposed. The inconsistency of the perovskite-post-perovskite heat model is proved. Calculations of inertia moments relative to the D boundary on the Earth are given. The 9 times difference allows us to claim that the sliding of the upper layers at the Earth's rotation speed variations emit heat by viscous friction.This heat is the basis of mantle convection and lithospheric plate tectonics.

The analysis is geometrically stable orbits of spacecraft remote sensing of the Еarth

2018 ◽  
Vol 15 (1) ◽  
pp. 12-22
Author(s):  
V. M. Artyushenko ◽  
D. Y. Vinogradov
Keyword(s):  
Remote Sensing ◽  
Gravitational Field ◽  
State Vector ◽  
Semimajor Axis ◽  
The State ◽  
Zonal Harmonics ◽  
The Earth ◽  
Conditions Of Stability

The article reviewed and analyzed the class of geometrically stable orbits (GUO). The conditions of stability in the model of the geopotential, taking into account the zonal harmonics. The sequence of calculation of the state vector of GUO in the osculating value of the argument of the latitude with the famous Ascoli-royski longitude of the ascending node, inclination and semimajor axis. The simulation is obtained the altitude profiles of SEE regarding the all-earth ellipsoid model of the gravitational field of the Earth given 7 and 32 zonal harmonics.

scholarly journals Geosystemics and Earthquakes

2018 ◽  
Author(s):  
Angelo De Santis ◽  
Gianfranco Cianchini ◽  
Rita Di Giovambattista ◽  
Cristoforo Abbattista ◽  
Lucilla Alfonsi ◽  
...  
Keyword(s):  
Dynamical System ◽  
Solid Earth ◽  
Case Studies ◽  
Central Italy ◽  
Point Of View ◽  
Earth System ◽  
Complex Dynamical System ◽  
The Earth ◽  
Earth’S Interior

Abstract. Geosystemics (De Santis 2009, 2014) studies the Earth system as a whole focusing on the possible coupling among the Earth layers (the so called geo-layers), and using universal tools to integrate different methods that can be applied to multi-parameter data, often taken on different platforms. Its main objective is to understand the particular phenomenon of interest from a holistic point of view. In this paper we will deal with earthquakes, considered as a long term chain of processes involving, not only the interaction between different components of the Earth’s interior, but also the coupling of the solid earth with the above neutral and ionized atmosphere, and finally culminating with the main rupture along the fault of concern (De Santis et al., 2015a). Some case studies (particular emphasis is given to recent central Italy earthquakes) will be discussed in the frame of the geosystemic approach for better understanding the physics of the underlying complex dynamical system.

Two Simplest Quadratic Chaotic Maps Without Equilibrium

2018 ◽  
Vol 28 (12) ◽  
pp. 1850144 ◽  
Author(s):  
Shirin Panahi ◽  
Julien C. Sprott ◽  
Sajad Jafari
Keyword(s):  
Dynamical System ◽  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Chaotic Maps ◽  
Basin Of Attraction ◽  
Hidden Attractor ◽  
Return Map ◽  
Right Hand ◽  
Dynamical Properties ◽  
The Right

Two simple chaotic maps without equilibria are proposed in this paper. All nonlinearities are quadratic and the functions of the right-hand side of the equations are continuous. The procedure of their design is explained and their dynamical properties such as return map, bifurcation diagram, Lyapunov exponents, and basin of attraction are investigated. These maps belong to the hidden attractor category which is a newly introduced category of dynamical system.

Neumayer, Humboldt and the search for a global physics

2011 ◽  
Vol 123 (1) ◽  
pp. 2
Author(s):  
R.W. Home
Keyword(s):  
Dynamical System ◽  
Research Program ◽  
Scientific Investigation ◽  
Point Of View ◽  
Mineral Deposits ◽  
New Mineral ◽  
Alexander Von Humboldt ◽  
The Earth

In setting up the Flagstaff Observatory in Melbourne in 1857, the young German geophysicist Georg Neumayer brought new standards of precision to the pursuit of physics in Australia. His wide-ranging research program in geomagnetism, meteorology and oceanography was conceived within an overall approach to science associated especially with the name of Alexander von Humboldt, that saw the Earth and its oceans and atmosphere as an integrated dynamical system. Neumayer also, however, envisaged immediate practical outcomes from his work, whether in determining optimal sailing routes between Europe and Australia, or in locating new mineral deposits. From a personal point of view he regarded his seven years in Australia as, above all, a preparation for the scientific investigation of Antarctica that he dreamed in vain of undertaking.

Motion of a satellite in the earth’s gravitational field

1960 ◽  
Vol 254 (1276) ◽  
pp. 48-65 ◽  
Keyword(s):  
Gravitational Field ◽  
Spherical Harmonics ◽  
Main Part ◽  
Equations Of Motion ◽  
Orbital Elements ◽  
Partial Derivatives ◽  
Rates Of Change ◽  
Zonal Harmonics ◽  
The Earth ◽  
Secular Terms

The equations of motion of a satellite are given in a general form, account being taken of the precession and nutation of the earth. The main part of the paper deals with the motion arising from the gravitational field of the earth, expressed as a general expansion in spherical harmonics. By evaluating the partial derivatives in Lagrange’s planetary equations, • expressions are obtained for the rates of change of the orbital elements. Particular consideration is given to the form of the expressions for the secular terms arising from the first four zonal harmonics.

scholarly journals Dynamical Complexity and Multistability in a Novel Lunar Wake Plasma System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Bo. Yan ◽  
Punam K. Prasad ◽  
Sayan Mukherjee ◽  
Asit Saha ◽  
Santo Banerjee
Keyword(s):  
Dynamical System ◽  
Lyapunov Exponents ◽  
Alpha Particles ◽  
Coexisting Attractors ◽  
Plasma System ◽  
Electrostatic Waves ◽  
Lunar Wake ◽  
Dynamical Complexity ◽  
Suprathermal Electrons ◽  
Different Types

Dynamical complexity and multistability of electrostatic waves are investigated in a four-component homogeneous and magnetized lunar wake plasma constituting of beam electrons, heavier ions (alpha particles, He++), protons, and suprathermal electrons. The unperturbed dynamical system of the considered lunar wake plasma supports nonlinear and supernonlinear trajectories which correspond to nonlinear and supernonlinear electrostatic waves. On the contrary, the perturbed dynamical system of lunar wake plasma shows different types of coexisting attractors including periodic, quasiperiodic, and chaotic, investigated by phase plots and Lyapunov exponents. To confirm chaotic and nonchaotic dynamics in the perturbed lunar wake plasma, 0−1 chaos test is performed. Furthermore, a weighted recurrence-based entropy is implemented to investigate the dynamical complexity of the system. Numerical results show existence of chaos with variation of complexity in the perturbed dynamics.

scholarly journals Resonant Orbital Dynamics in LEO Region: Space Debris in Focus

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
J. C. Sampaio ◽  
E. Wnuk ◽  
R. Vilhena de Moraes ◽  
S. S. Fernandes
Keyword(s):  
Collision Avoidance ◽  
Frequency Analysis ◽  
Space Debris ◽  
Semimajor Axis ◽  
Orbital Dynamics ◽  
Accurate Information ◽  
The Earth ◽  
Low Earth Orbits ◽  
Line Elements ◽  
Earth Orbits

The increasing number of objects orbiting the earth justifies the great attention and interest in the observation, spacecraft protection, and collision avoidance. These studies involve different disturbances and resonances in the orbital motions of these objects distributed by the distinct altitudes. In this work, objects in resonant orbital motions are studied in low earth orbits. Using the two-line elements (TLE) of the NORAD, resonant angles and resonant periods associated with real motions are described, providing more accurate information to develop an analytical model that describes a certain resonance. The time behaviors of the semimajor axis, eccentricity, and inclination of some space debris are studied. Possible irregular motions are observed by the frequency analysis and by the presence of different resonant angles describing the orbital dynamics of these objects.

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