In this paper, smooth Chua’s equation is generalized to a higher order system from a special viewpoint of interconnected systems. Simple conditions for Lagrange stability are established. And a detailed Lagrange stable region analysis is given for the canonical Chua’s oscillator. In addition, a new nonlinearly coupled Chua’s circuit that appeared in the recent literature is also discussed and a...

the application of inertial stabilization system is to stabilize the sensor’s line of sight toward a target by isolating the sensor from the disturbances induced by the operating environment. The aim of this paper is to present two axes gimbal system. The equations of gimbals motion are derived using Lagrange equation considering the base angular motion and mass unbalance. The stabilization loo...

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 inclinations. The model, which is valid in the entire co-orbital region, possesses an integrable approximation modeling the planar and quasi-circular motions...

Enlightened from the inverse consideration of the stable continuous-time dynamics evolution, the Variation Evolving Method (VEM) analogizes the optimal solution to the equilibrium point of an infinite-dimensional dynamic system and solves it in an asymptotically evolving way. In this paper, the compact version of the VEM is further developed for the computation of Optimal Control Problems (OCPs...

In this paper we study the dynamics of some second order Lagrangians that come from Pfaff forms, i.e. differential forms on tangent bundles. In the non-singular case, mainly considered in the paper, the generalized Euler-Lagrange equation is a third order differential equation. We prove that the solutions of the differential equations of motion of a charge in a field and the Euler equations of ...

Motion analysis in computer vision is a well-studied problem with numerous applications. In particular, the tasks of optical flow estimation and tracking are of increasing interest. In this paper, we propose a level set approach to address both aspects of motion analysis. Our approach relies on the propagation of smooth interfaces to perform tracking while using an incremental estimation of the...

We propose and solve a synchronized path following problem for a differential drive robot modeled as a dynamic unicycle and an Euler-Lagrange system. Each system is assigned a simple closed curve in its output space. The outputs of systems must approach and traverse their assigned curves while synchronizing their motions along the paths. The synchronization problems we study in this thesis incl...

Particle-laden or droplet-laden turbulent flows occur in many industrial applications and in natural phenomena. Knowledge about the properties of these flows can help to improve the design of unit operations in industry and to predict for instance the occurrence of rain showers. This knowledge can be obtained from experimental research and from numerical simulations. In this paper a review is g...

in this paper, we propose the chebyshev wavelet approximation for the numerical solution of a class of integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. we show that the chebyshev approximation transform an integral equation to an explicit system of linear algebraic equations. illustrative examples are included t...