We study the phase space dynamics of multi–dimensional symplectic maps, using the method of the Generalized Alignment Index (GALI). In particular, we investigate the behavior of the GALI for a system of N = 3 coupled standard maps and show that it provides an efficient criterion for rapidly distinguishing between regular and chaotic motion.

Pavement surface unevenness plays a pivotal role on roughness index of road which affects on riding comfort ability. Comfort ability refers to the degree of protection offered to vehicle occupants from uneven elements in the road surface. So, it is preferable to have a lower roughness index value for a better riding quality of road users. Roughness is generally defined as an expression of irreg...

The existence of harmonics will cause the quality power supply in a system to decline and affect normal use system. Therefore, it is important suppress system, first step harmonic suppression detection. To address this phenomenon, fast detection method proposed paper. It based on input observer theory construct state space model original signal components estimate variables so as achieve extrac...

Given an ordinary differential equation on a homogeneous manifold, one can construct a “geometric integrator” by determining a compatible ordinary differential equation on the associated Lie group, using a Lie group integration scheme to construct a discrete time approximation of the solution curves in the group, and then mapping the discrete trajectories onto the homogeneous manifold using the...

In this paper, we consider the development of an extended block integrator for the solution of stiff and oscillatory first-order Ordinary Differential Equations (ODEs) using interpolation and collocation techniques. The integrator was developed by collocation and interpolation of the combination of power series and exponential function to generate a continuous implicit Linear Multistep Method (...

Is is known that the loop space associated to a Riemannian manifold admits a quasi-symplectic structure. This article shows that this structure is not likely to recover the underlying Riemannian metric by proving a result that is a strong indication of the “almost” independence of the quasi-symplectic structure with respect to the metric. Finally conditions to have contact structures on these s...

Knowledge of accuracy of numerical integration is important for composing an overall numerical error budget; in orbit determination and propagation for space surveillance, there is frequently a computation time-accuracy tradeoff that must be balanced. There are several techniques to assess the accuracy of a numerical integrator. In this paper we compare some of those techniques: comparison with...

We give an intrinsic proof that Vorobjev’s first approximation of a Poisson manifold near a symplectic leaf is a Poisson manifold. We also show that Conn’s linearization results cannot be extended in Vorobjev’s setting

Various faults and disturbances often make the grid unbalanced distorted. To grid-connected converters resilient to distorted grid, real-time estimation of voltage sequences are essential. Adaptive-observer based grid-synchronization techniques very suitable for this purpose. In paper, a comparative analysis three recently proposed adaptive observer-based technique presented frequency sequence ...

Motivated by the GKM picture of the equivariant cohomol-ogy ring for a torus action on an orbifold we define one-skeletons and their corresponding rings, H(Γ, α). We prove that, under a mild gener-icity condition, such a ring is a free S(g *)−module, with generators given by Thom classes of flow-outs of the vertices. We also show that many interesting notions and results in symplectic geometry,...