Lie Group and Lie Algebra Variational Integrators for Flexible Beam and Plate in R3
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The underlying goal of this Master's thesis is of laying down, in so far as possible, the foundations for later work in Geometric Stochastic Mechanics. The first part is a presentation of symplectic reduction, going through the momentum map and culminating ...
The equilibrium position of an Euler-Bernoulli beam is investigated. Using the discrete Euler-Lagrange and Lagrange-d’Alembert principles, the behavior of the beam is simulated using variational integrators and, in particular, AVIs (Asynchronous Variationa ...
This is an interdisciplinary research project. This proposal presents research directions in the mechanics of thin-shell and rod theory by using the formalism of discrete mechanics applied to the study of structures in civil engineering. Its aims are to co ...
The purpose of this research project is to develop variational integrators synchronous or asynchronous, which can be used as tools to study complex structures composed of plates and beams subjected to large deformations and stress. We consider the geometri ...
Stiffness tomography is a new atomic force microscopy imaging technique that allows highlighting structures located underneath the surface of the sample. In this imaging mode, such structures are identified by investigating their mechanical properties. We ...
A theorem of Drinfel'd (Drinfel'd (1993)) classifies the Poisson homogeneous spaces of a Poisson Lie group (G,πG) via a special class of Lagrangian subalgebras of the Drinfel'd double of its Lie bialgebra. This result is extended in Liu et al. (1998) to a ...
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 approach formulat ...
The regular reduction of a Dirac manifold acted upon freely and properly by a Lie group is generalized to a nonfree action. For this, several facts about G-invariant vector fields and one-forms are shown. ...
Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as ...
We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincar, equations on Lie groups and homogeneous spaces. Orbit invariants play an impor ...