相关论文: Orbit Dynamics for Unstable Linear Motion

This paper defines the beta function and other linear orbit parameters using the exact equations of motion. The orbit functions are redefined using the exact equations. Expressions are found for the transfer matrix and the emittances.…

A novel technique to determine invariant curves in nonlinear beam dynamics based on the method of formal series has been developed. It is first shown how the solution of the Hamilton equations of motion describing nonlinear betatron…

The paper shows sufficiency conditions for stability of continuous periodic orbits under phase uncertainty. Phase based uncertainty is a trait of bipedal walking robots, where the desired trajectories are parameterized by a monotonous…

Stable and unstable manifolds, originating from hyperbolic cycles, fundamentally characterize the behaviour of dynamical systems in chaotic regions. This letter demonstrates that their shifts under perturbation, crucial for chaos control,…

We study the motion of an incompressible, inviscid two-dimensional fluid in a rotating frame of reference. There the fluid experiences a Coriolis force, which we assume to be linearly dependent on one of the coordinates. This is a common…

For a one-dimensional motion, a constant of motion for non autonomous an linear system (position and velocity) is given from the constant of motion associated to its autonomous system. This approach is used in the study of the harmonic…

The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…

The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model…

Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles…

In laboratory studies and numerical simulations, we observe clear signatures of unstable time-periodic solutions in a moderately turbulent quasi-two-dimensional flow. We validate the dynamical relevance of such solutions by demonstrating…

The invariant manifold approach is used to explore the dynamics of a nonlinear rotor, by determining the nonlinear normal modes, constructing a reduced order model and evaluating its performance in the case of response to an initial…

We present a complete analysis of the linearised dynamics of active solids with orientational order, taking into account a hitherto overlooked consequence of rotation invariance. Our predictions include the possibility of stable active…

Based on the technique of the discrete one-turn transfer maps, the problem of linear coupling between horizontal and vertical betatron oscillations in an accelerator has been treated exactly and entirely in explicit form. The stability…

We study the motion of test particles around a center of attraction represented by a monopole (with and without spheroidal deformation) surrounded by a ring, given as a superposition of Morgan & Morgan discs. We deal with two kinds of…

Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…

Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the…

We numerically investigate the dynamics of orbits in 3D circumbinary phase-space as a function of binary eccentricity and mass fraction. We find that inclined circumbinary orbits in the elliptically-restricted three-body problem display a…

Depending on the involved physiobiological parameters, stable or unstable behavior in active fluids is observed. In this paper a rigorous analytical justification of (in-)stability within the corresponding regimes is given. In particular,…

We study in this article the mathematical properties of a class of orbital-free kinetic energy functionals. We prove that these models are linearly stable but nonlinearly unstable, in the sense that the corresponding kinetic energy…

We study the beta functions for the dimensionless couplings in quadratic curvature gravity, and find that there is a simple argument to restrict the possible form of the beta functions as derived from the counterterms at an arbitrary loop.…