Variations of the Poincaré Map
نویسنده
چکیده
Nogueira, in 1995, presented a study of the Poincaré map and the related ParryDaniels map. In this note some variants of this algorithm are presented which seem to have quite different ergodic behavior.
منابع مشابه
Analysis of 3D Passive Walking Including Turning Motions for the Finite-width Rimless Wheel
The focus of studies in the field of passive walking has often been on straight walking, while less attention has been paid to the field of turning motions. In this paper, the passive motions of a finite width rimless wheel as the simplest 3D model of passive biped walkers was investigated with a focus on turning motions. For this purpose, the hybrid model of the system consisting of continuous...
متن کاملStable Gait Planning and Robustness Analysis of a Biped Robot with One Degree of Underactuation
In this paper, stability analysis of walking gaits and robustness analysis are developed for a five-link and four-actuator biped robot. Stability conditions are derived by studying unactuated dynamics and using the Poincaré map associated with periodic walking gaits. A stable gait is designed by an optimization process satisfying physical constraints and stability conditions. Also, considering...
متن کاملThe Reduced Euler-Lagrange Equations
Marsden and Scheurle [1993] studied Lagrangian reduction in the context of momentum map constraints—here meaning the reduction of the standard Euler-Lagrange system restricted to a level set of a momentum map. This provides a Lagrangian parallel to the reduction of symplectic manifolds. The present paper studies the Lagrangian parallel of Poisson reduction for Hamiltonian systems. For the reduc...
متن کاملOn the calculation of the linear stability parameter of periodic orbits
In this paper we propose an improved method for calculating Hénon’s stability parameter, which is based on the differential of the Poincaré map using the first variational equation. We show that this method is very accurate and give some examples where it gives correct results, while the previous method could not cope.
متن کاملClassifying the Epilepsy Based on the Phase Space Sorted With the Radial Poincaré Sections in Electroencephalography
Background: Epilepsy is a brain disorder that changes the basin geometry of the oscillation of trajectories in the phase space. Nevertheless, recent studies on epilepsy often used the statistical characteristics of this space to diagnose epileptic seizures. Objectives: We evaluated changes caused by the seizures on the mentioned basin by focusing on phase space sorted by Poincaré sections. Ma...
متن کامل