Related papers: Hill's formula

We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill…

We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…

We investigate Hill's lunar equations, series and the motion of the perigee, and we use computers to go farther than has previously been known, calculating the coefficients of Hill's series up to order 24 in m, and the coefficients that do…

We study the effects of general relativistic gravity on the Hill stability, that is, the stability of a multi-body system against a close approach of one orbit to another, which has been hitherto studied mainly in Newtonian mechanics and…

The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical…

Our previous study of a system of bodies assumed to move along almost circular orbits around a central mass, approximately described by Hill's equations, is extended to "exotic" [alias non-commutative] particles. For a certain critical…

We review some recent progress on the research of the periodic orbits of the N-body problem,and propose a numerical scheme to determine the spatial doubly-symmetric periodic orbits (SDSPs for short). Both comet- and lunar-type SDSPs in the…

An extension of Riewe's fractional Hamiltonian formulation is presented for fractional constrained systems. The conditions of consistency of the set of constraints with equations of motion are investigated. Three examples of fractional…

In this paper we show the existence of syzygies for all periodic orbits inside the bounded Hill's region of the planer circular restricted three-body problem with energy below the second critical value. The proof will follow some ideas of…

A method for deriving superintegrable Hamiltonians with a spin orbital interaction is presented. The method is applied to obtain a new superintegrable system in Euclidean space $\mathbb{E}_3$ with the following properties. It describes a…

An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…

We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitude, is expanded in power series of eccentricities and…

We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…

In this work, we investigate generic classical two-dimensional (2D) superintegrable Hamiltonian systems H, characterized by the existence of three functionally independent integrals of motion (I_0=H,I_1,I_2). Our main result, formulated and…

For several objects of interest in geometric complexity theory, namely for the determinant, the permanent, the product of variables, the power sum, the unit tensor, and the matrix multiplication tensor, we introduce and study a fundamental…

We study the Hamiltonian formalism for second order and fourth order nonlinear Schr\"{o}dinger equations. In the case of second order equation, we consider cubic and logarithmic nonlinearities. Since the Lagrangians generating these…

In this work the existence of periodic solutions is studied for the Hamiltonian functions (Formula presented.) where the first term consist of a harmonic oscillator and the second term are homogeneous polynomials of degree 5 defined by two…

In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…

A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occur in a pairwise fashion. It is also…