Leitz T (2022)
Publication Language: English
Publication Type: Thesis
Publication year: 2022
This thesis starts with overview of the fundamentals of Lie groups and quaternions in order to
give readers a smooth entry to the later chapters. Therein the central concept of a constraint
Lie group and the relationship with the null space method are explained with examples.
It follows an introduction to continuous mechanics on Lie groups, Hamiltonian mechanics
and Nother’s theorem. This topic is then extended to a two-dimensional space-time to later
allow the modelling of geometrically exact beams.
In order to derive a variational Lie group integrator, a discrete version of the forementioned
Lagrangian mechanics is introduced, together with the necessary interpolation methods for the
derivation of the Galerkin basis functions. Computational approaches for solving the discrete
Euler-Lagrange equations are discussed. The derived method is then compared to the discrete
null-space method and the well-known RATTLE algorithm.
The work concludes with the application of the method in the form of numerical examples
to simulate rigid body dynamics (as an example of a Galerkin Lie group integrator) and
geometrically
APA:
Leitz, T. (2022). Galerkin Lie group variational integrators (Dissertation).
MLA:
Leitz, Thomas. Galerkin Lie group variational integrators. Dissertation, 2022.
BibTeX: Download