overview of lie group variational integrators and their applications to ...

In §3, we explicitly construct a Lie group variational integrator for the full body problem from celestial mechanics, and perform an in depth numerical ...

Lie Group Variational Integrators and their Applications to Optimal ...

An Overview of Lie Group Variational Integrators and their Applications to Optimal Control ... West Lafayette, Indiana, USA. ... This is achieved by constructing G- ...

An introduction to Lie group integrators - basics, new developments ...

presented and the notion of discrete gradient methods is generalised to Lie groups. ... integrators for Hamiltonian problems, considering the ...

Lie group variational integrators for the full body problem

They reduce the discrete dynamics on a Lie group to the dynamics on the corresponding Lie algebra. Sanyal, Shen and McClamroch develop variational integrators ...

arXiv:2201.10768v1 [math.NA] 26 Jan 2022

The main disadvantage of Galerkin Lie group variational integrators is the term dexp in (3). This implies that the resulting discrete Euler ...

Lie Group and Homogeneous Variational Integrators

... application of the ... Summary. □ Lie group variational integrators. • A combination of Lie group ideas with variational integrators, with the properties:.

[PDF] An introduction to Lie group integrators - Semantic Scholar

The main purpose of this paper is to test the performance of Lie group integrators as applied to a semi-discrete version of the KdV equation. 5 Citations.

Lie group integrator - Wikipedia

A Lie group integrator is a numerical integration method for differential equations built from coordinate-independent operations such as Lie group actions ...

A Lie group variational integration approach to the full discretization ...

As an alternative to this brute force approach, the nonlinear structure of the configuration space may be addressed directly using Lie group ...

[1207.0069] An introduction to Lie group integrators - arXiv

Abstract:We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are ...

Hamilton–Pontryagin Integrators on Lie Groups Part I

Included among these integrators are generalizations of symplectic Euler and Störmer–Verlet integrators from flat spaces to Lie groups. Because of their ...

Lie Group Integrators for Animation and Control of Vehicles

and Lie group variational integrators in Sec. 2, we present a formal, general treatment of the discrete variational principles used to derive our ...

Full article: Lie group integrators for mechanical systems

There is a natural symplectic structure on such manifolds and through variational principles one may derive symplectic Lie group integrators. We also consider ...

Lie Group Variational Collision Integrators for Hybrid Systems

Lie group variational collision integrators provide symplectic, momentum-preserving solutions for hybrid systems with sharp corner impacts. Abstract. The ...

An introduction to Lie group integrators – basics, new developments ...

Crouch and Grossman [22] suggested to advance the numerical solution by computing flows of vector fields in some Lie algebra. Lewis and Simo [45] ...

Lie Group Forced Variational Integrator Networks for Learning and ...

More specifically, we extend the discrete-time Euclidean formulation of FVINs with control from. (Havens and Chowdhary, 2021) to Lie groups in a structure- ...

A lie group variational integrator for the attitude dynamics of a rigid ...

Since their introduction, Lie group integrators have become a method of choice in many application areas. Various formulations of these integrators exist ...

Lie Group Variational Integrators for the Full Body Problem

... The use of Lie group SE(3) enables guidance, navigation, and control algorithms to be built within this framework and enables the consideration of coupled ...

A Lie group variational integrator for rigid body motion in SE(3) with ...

We use a discretization scheme for such systems which is based on the discrete Lagrange-d'Alembert principle to obtain the Lie group variational integrator. We ...

Schedule And Notes Detail - SLMath

In contrast to traditional Lie group integrators, issues of equivariance and order-of-accuracy are independent of the choice of retraction in the variational ...