Diverse Tools and Functionalities

Diverse Tools and Functionalities

This page gives an overview over the additional functionalities which have been introduced for handling and analysing the dynamics on invariant manifolds. They aid in visualisation of results, manipulation of the manifold parametrisation, among others.

Contents

Dynamical System Analysis

For the general analysis of the behaviour of the dynamical system, and the dynamics on it in relation to the dynamics on the invariant manifolds, the following functions have been written.

ROMs

Several functions are especially dedicated to the analysis of the reduced dynamics on the SSM and to mapping the results of the analysis from the parametrisation space back to the physical phase space.

Visualisation

The following functions serve for the visualisation of results and of the manifold itself.

Nonlinear Maps

The following functions are designed to handle and convert nonlinear functions, such as the internal forces or the parametrisation coefficients. They are employed to evaluate mult-index expansions, convert them into a tensor - based representation, and for multi-variable calculus.

Further tools