We show that the minimization of the Lagrangian action functional on suitable classes of symmetric loops yields collisionless periodic orbits of the n-body problem, provided that some simple conditions on the symmetry group are satisfied. More precisely, we give a fairly general condition on symmetry groups G of the loop space Λ for the n-body problem (with potential of homogeneous degree −α, w...

We consider planar and spatial autonomous Newtonian systems with Coriolis forces study the existence of branches periodic orbits emanating from equilibria. investigate both degenerate nondegenerate situations. While Lyapunov's center theorem applies locally in nondegenerate, nonresonant context, our result provides a global answer which is significant also some cases. apply abstract results to ...

Analytical solutions to a variety of simplified versions the restricted three-body problem in celestial mechanics possess long running history that encompasses several centuries. Most successes were limited either planar configuration three bodies, motion around Lagrange points, or Kozai–Lidov effect. We review some analytical advances obtained by separating rapid and slow subsystems as present...

A recent analysis of two handwritten sheets paper by Henry Cavendish (1731–1810) reveals the details his calculation deflection light induced gravitational field isolated celestial bodies. Except for a few lines from one these pages, where communicated result, documents have never been published. This gave rise to speculations about how, if at all, derived formula angle own calculations. Such d...

Isochrone potentials, as defined by Michel H\'enon in the fifties, are spherically symmetric potentials within which a particle orbits with radial period that is independent of its angular momentum. encompass Kepler and harmonic potential, along many other. In this article, we revisit classical problem motion isochrone from point view Hamiltonian mechanics. First, use particularly well-suited s...

We generalize the first law of black hole mechanics to rotating, charged C-metric and Ernst metric, both which have as a special case. All these metrics are (3+1)-dimensional, vanishing cosmological constant, physically describe pair holes pulled apart null infinity by some external force. Our laws global in sense applying an entire patch spacetime, opposed neighborhood hole. They formulated wi...

The study of the phase space multidimensional systems is one central open problems in dynamical systems. Being able to distinguish chaoticity from regularity nonlinear systems, as well determine subspace which instabilities are expected occur, also an important field. To investigate these, diverse chaos indicators have been developed. information provided these understand behaviour many celesti...