Related papers: Lie Group Spectral Variational Integrators

We develop the structure theory of symplectic Lie groups based on the study of their isotropic normal subgroups. The article consists of three main parts. In the first part we show that every symplectic Lie group admits a sequence of…

We classify solvable Lie groups admitting left invariant symplectic half-flat structure. When the Lie group has a compact quotient by a lattice, we show that these structures provide solutions of supersymmetric equations of type IIA.

We introduce generalized Galerkin variational integrators, which are a natural generalization of discrete variational mechanics, whereby the discrete action, as opposed to the discrete Lagrangian, is the fundamental object. This is achieved…

We introduce a novel numerical method to integrate partial differential equations representing the Hamiltonian dynamics of field theories. It is a multi-symplectic integrator that locally conserves the stress-energy tensor with an excellent…

We present a combination of tools which allows for investigation of the coupled orbital and rotational dynamics of two rigid bodies with nearly arbitrary shape and mass distribution, under the influence of their mutual gravitational…

We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit…

We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by means of the adjoint representations of Lie algebras. In this way, we calculate some compatible Poisson structures on four dimensional and…

In this paper, we describe procedures for computing higher-order time derivatives of the Lie-group Newton-Euler, Articulated-Body Inertia, and hybrid dynamics algorithms for floating-base trees, where the base configuration evolves on SE(3)…

We show that a Lie algebroid on a stratified manifold is integrable if, and only if, its restriction to each strata is integrable. These results allow us to construct a large class of algebras of pseudodifferential operators.

We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories…

In this paper, we investigate the integrability aspects of a physically important nonlinear oscillator which lacks sufficient number of Lie point symmetries but can be integrated by quadrature. We explore the hidden symmetry, construct a…

We present a new class of exponential integrators for ordinary differential equations: locally exact modifications of known numerical schemes. Local exactness means that they preserve the linearization of the original system at every point.…

We present a general framework for constructing structure-preserving numerical integrators for nonholonomically constrained mechanical systems evolving on Lie groups using retraction maps. Retraction maps generalize the exponential map and…

Numerical algorithms based on variational and symplectic integrators exhibit special features that make them promising candidates for application to general relativity and other constrained Hamiltonian systems. This paper lays part of the…

We investigate higher-order geometric $k$-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images, e.g., in longitudinal studies of Computational Anatomy. Our…

We prove an equivariant implicit function theorem for variational problems that are invariant under a varying symmetry group (corresponding to a bundle of Lie groups). Motivated by applications to families of geometric variational problems…

In this work we deal with left invariant complex and symplectic structures on simply connected four dimensional solvable real Lie groups. We search the general form of such structures, when they exist and we make use of this information to…

We explore the integration of representations from a Lie algebra to its algebraic group in positive characteristic. An integrable module is stable under the twists by group elements. Our aim is to investigate cohomological obstructions for…

Variational integrators are a special kind of geometric discretisation methods applicable to any system of differential equations that obeys a Lagrangian formulation. In this thesis, variational integrators are developed for several…

A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…