Results 271 to 280 of about 13,491,973 (291)

Lie Group Spectral Variational Integrators

Foundations of Computational Mathematics, 2014
We present a new class of high-order variational integrators on Lie groups. We show that these integrators are symplectic and momentum-preserving, can be constructed to be of arbitrarily high order, or can be made to converge geometrically.
James Hall, M. Leok
semanticscholar   +1 more source

The Lie group of bisections of a Lie groupoid

, 2014
In this article, we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebra of sections of the associated Lie algebroid and show ...
Alexander Schmeding, Christoph Wockel
semanticscholar   +1 more source

Elementary Lie Group Analysis and Ordinary Differential Equations

, 1999
Introduction to Differential Equations. Transformation Groups. Lie Group Analysis of Ordinary Differential Equations. Brief on Lie Algebras. First Order Differential Equations. Integration of Second Order Equations.
N. Ibragimov
semanticscholar   +1 more source

Two Lie Group Formulations for Dynamic Multibody Systems With Large Rotations

, 2011
This paper studies the formulation of the dynamics of multibody systems with large rotation variables and kinematic constraints as differential-algebraic equations on a matrix Lie group.
O. Bruls, M. Arnold, A. Cardona
semanticscholar   +1 more source

On a Compact Lie Group Acting on a Manifold

, 1957
Let M be a manifold (= connected, separable, locally euclidean space) of dimension n + 1, and G a compact connected Lie group acting on M in such a way that there is at least one n-dimensional orbit.2 In this paper, we show that the space of orbits M/G ...
P. Mostert
semanticscholar   +1 more source

Integrability of Poisson–Lie Group Actions

, 2009
We establish a 1:1 correspondence between Poisson–Lie group actions on integrable Poisson manifolds and twisted multiplicative Hamiltonian actions on source 1-connected symplectic groupoids. For an action of a Poisson–Lie group G on a Poisson manifold M,
R. Fernandes, David Iglesias Ponte
semanticscholar   +1 more source

The heat equation on compact Lie group

, 1975
McKean and Singer [9] posed the problem of the existence of an analogue of the Poisson's summation formula for manifolds other than flat tori. Y. Colin de Verdiere [3] gave an answer to it in the case of a 2-dimensional compact Riemannian manifold with ...
H. Urakawa
semanticscholar   +1 more source

The Lie group of Newton's and Lagrange's equations for the harmonic oscillator

, 1976
Lie's theory of differential equations is applied to the equation of motion of the classical one-dimensional harmonic oscillator. The equation is found to be invariant under a global Lie group of point transformations that is shown to be SL(3, R).
C. Wulfman, B. G. Wybourne
semanticscholar   +1 more source

Consistent EKF-Based Visual-Inertial Odometry on Matrix Lie Group

IEEE Sensors Journal, 2018
Se-jong Heo, Chan Gook Park
semanticscholar   +1 more source

On the tangent Lie group of a symplectic Lie group

Ricerche di Matematica, 2019
D. Pham
semanticscholar   +1 more source