Lyapunov stability for a generalized Hénon-Heiles system in a rotating reference frame
نویسندگان
چکیده
In this paper we focus on a generalized Hénon–Heiles system in a rotating reference frame, in such a way that Lagrangian-like equilibrium points appear. Our goal is to study their nonlinear stability properties to better understand the dynamics around these points. We show the conditions on the free parameters to have stability and we prove the superstable character of the origin for the classical case; it is a stable equilibrium point regardless of the frequency value of the rotating frame. 2014 Elsevier Inc. All rights reserved.
منابع مشابه
Power Swings Damping Improvement with STATCOM and SMES Based on the Direct Lyapunov Method
In this paper a comprehensive approach is presented to improve power swings damping based on direct Lyapunov method. The approach combines superconducting magnetic energy storage (SMES) system with static synchronous compensator (STATCOM). Considering the energy absorption/injection ability of SMES, in transient states the combination exchanges both active and reactive powers with power system....
متن کاملIntegration of a generalized Hénon-Heiles Hamiltonian
The generalized Hénon-Heiles Hamiltonian H = 1/2(P 2 X + P 2 Y + c1X 2 + c2Y 2) + aXY 2 − bX3/3 with an additional nonpolynomial term μY −2 is known to be Liouville integrable for three sets of values of (b/a, c1, c2). It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton-Jacobi equations, we succeed here, in...
متن کاملSmaller alignment index ( SALI ) : Determining the ordered or chaotic nature of orbits in conservative dynamical systems
We apply the smaller alignment index (SALI) method for distinguishing between ordered and chaotic motion in some simple conservative dynamical systems. In particular we compute the SALI for ordered and chaotic orbits in a 2D and a 4D symplectic map, as well as a two–degree of freedom Hamiltonian system due to Hénon & Heiles. In all cases, the SALI determines correctly the nature of the tested o...
متن کاملHénon–heiles Hamiltonian for Coupled Upper–hybrid and Magnetoacoustic Waves in Magnetized Plasmas
We show that the coupled mode equations for the stationary propagation of upper–hybrid and magnetoacoustic waves in magnetized electron–ion plasmas with negative group dispersion can be exactly derived from the generalized Hénon–Heiles Hamiltonian. The parameter regimes for the integrable cases of the coupled mode equations have been explicitly obtained. For positive group dispersion of the upp...
متن کاملRobust Lyapunov-based Control of MEMS Optical Switches
In this paper, a robust PID control scheme is proposed for Micro-Electro-Mechanical-Systems (MEMS) optical switches. The proposed approach is designed in a way which solves two challenging and important problems. The first one is successful reference tracking and the second is mitigating the system nonlinearities. The overall system composed of nonlinear MEMS dynamics and the PID controller is ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 253 شماره
صفحات -
تاریخ انتشار 2015