Lie group dynamics of reduced multibody-fluid systems

Dynamics of Multibody Systems

Dynamics and Control of Multibody Systems

Reduction of Dynamics with Lie Group Analysis

This paper is mainly a review concerning singular perturbation methods by means of Lie group analysis which has been presented by the author. We make use of a particular type of approximate Lie symmetries in those methods in order to construct reduced systems which describe the longtime behavior of the original dynamical system. Those methods can be used in analyzing not only ordinary different...

The Lie Group of Fourier Integral Operators * and Applications to Fluid Dynamics

Lie Point Symmetries for Reduced Ermakov Systems

Reduced Ermakov systems are defined as Ermakov systems restricted to the level surfaces of the Ermakov invariant. The condition for Lie point symmetries for reduced Ermakov systems is solved yielding four infinite families of systems. It is shown that SL(2, R) always is a group of point symmetries for the reduced Ermakov systems. The theory is applied to a model example and to the equations of ...