A flexible error estimate for the application of centre manifold theory
نویسندگان
چکیده
In applications of centre manifold theory we need more flexible error estimates than that provided by, for example, the Approximation Theorem 3 by Carr [4, 6]. Here we extend the theory to cover the case where the order of approximation in parameters and that in dynamical variables may be completely different. This allows, for example, the effective evaluation of low-dimensional dynamical models at finite parameter values. Maths Subj. Class: 37L10, 37N10.
منابع مشابه
Evaluation of the Centre Manifold Method for Limit Cycle Calculations of a Nonlinear Structural Wing
In this study the centre manifold is applied for reduction and limit cycle calculation of a highly nonlinear structural aeroelastic wing. The limit cycle is arisen from structural nonlinearity due to the large deflection of the wing. Results obtained by different orders of centre manifolds are compared with those obtained by time marching method (fourth-order Runge-Kutta method). These comparis...
متن کاملSoil and Rock Slope Stability Analysis based on Numerical Manifold Method and Graph Theory
Limit equilibrium method, strength reduction method and Finite Difference Methods are the most prevalently used methods for soil and rock slope stability analysis. However, it can be mention that those have some limitations in practical application. In the Limit equilibrium method, the constitutive model cannot be considered and many assumptions are needed between slices of soil and rock. The s...
متن کاملApplication of Support Vector Machine Regression for Predicting Critical Responses of Flexible Pavements
This paper aims to assess the application of Support Vector Machine (SVM) regression in order to analysis flexible pavements. To this end, 10000 Four-layer flexible pavement sections consisted of asphalt concrete layer, granular base layer, granular subbase layer, and subgrade soil were analyzed under the effect of standard axle loading using multi-layered elastic theory and pavement critical r...
متن کاملNORMAL FORM SOLUTION OF REDUCED ORDER OSCILLATING SYSTEMS
This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamical systems. Limit cycle oscillations are determined for simple two-degree-of-freedom double pendulum systems. The double pendulum system is reduced into its centre manifold before computing normal forms. Normal forms are obtained using a period averaging method which is appl...
متن کاملReduced order model for doubly output induction generator in wind park using integral manifold theory
A dynamic reduced order model using integral manifold theory has been derived, which can be used to simulate the DOIG wind turbine using a double-winding representation of the generator rotor. The model is suitable for use in transient stability programs that can be used to investigate large power systems. The behavior of a wind farm and the network under various system disturbances was stu...
متن کامل