The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications various areas study such as celestial mechanics, fluid Steller structure, isothermal gas spheres, thermionic currents so on. Because importance equation, method generalized Sundman transformation (GST) proposed by Nakpim Meleshko used for linearizin...

Steepness is a generic geometric property which, together with complex-analyticity, needed in order to ensure stability of nearly-integrable hamiltonian system over exponentially long times. Following strategy developed by Nekhoroshev, we construct sufficient conditions for steepness given function that involve algebraic equations on its derivatives up five. This important view applications (e....

The Hannay angle has been previously studied for a celestial circular restricted three-body system by means of an adiabatic approach. In this work, three main results are obtained. Firstly, a formal connection between perturbation theory and the Hamiltonian adiabatic approach, both leading to the Hannay angle; it is thus emphasised that this effect is already contained in classical celestial me...

Geodesy is the science of the measurement and mapping of the Earth’s surface, and in this context it is also the science that defines and realizes coordinates and associated coordinate systems. Geodesy thus is the foundation for all applications of GNSS. This chapter presents the reference systems needed to describe coordinates of points on the Earth’s surface or in near space and to relate coo...

In contact Hamiltonian systems, the so-called dissipated quantities are akin to conserved in classical systems. this article, a Noether's theorem for non-autonomous systems is proved, characterizing class of symmetries which bijection with quantities. Other classes preserve (up conformal factor) additional structures, such as form or function, also studied. Furthermore, making use geometric str...

The Hannay angle has been previously studied for a celestial circular restricted three-body system by means of an adiabatic approach. In the present work, three main results are obtained. Firstly, a formal connection between perturbation theory and the Hamiltonian adiabatic approach shows that both lead to the Hannay angle; it is thus emphasised that this effect is already contained in classica...

A bstract We examine the structure of global conformal multiplets in 2D celestial CFT. For a 4D bulk theory containing massless particles spin s = $$ \left\{0,\frac{1}{2},1,\frac{3}{2},2\right\} 0 1 2 3 we...

A wave function can be written in the form of {\psi} = ReiS/h. We put this into quantum mechanics equations and take hydrodynamic limit, i. e., let Planck constant zero. Then motion (EOM) describing movement macroscopic bodies are retrieved. From Schrodinger equation, we obtain Newtonian mechanics, including Newtons three laws motion; from decouple Klein-Gordon equation with positive kinetic en...

The Hannay angle has been previously studied for a celestial circular restricted three-body system by means of an adiabatic approach. In this work, three main results are obtained. Firstly, a formal connection between perturbation theory and the Hamiltonian adiabatic approach, both leading to the Hannay angle; it is thus emphasised that this effect is already contained in classical celestial me...