Seminario de Pre-Lectura de Tesis
Título: "Geometric and numerical analysis of nonholonomic systems"
Ponente: Alexandre Anahory Simoes (ICMAT-UAM).
Directores: David Martín de Diego (ICMAT-CSIC) y Juan Carlos Marrero (Universidad de La Laguna).
Abstract: In this thesis, we deduced new geometric and analytical properties
of nonholonomic systems which hopefully will provide a new insight into the subject. Firstly, we define
the nonholonomic exponential map which plays a role in the
description of nonholonomic trajectories as well as on applications to numerical
analysis. After introducing this new object, the thesis may be divided
into two parts. In the first part, we present new geometric properties of mechanical nonholonomic
systems such as the existence of a constrained Riemannian manifold
containing radial nonholonomic trajectories with fixed starting point and on
which they are geodesics. This is a new and surprising result because it
opens the possibility of applying variational techniques to nonholonomic dynamics,
which is commonly seen to be non-variational in nature. Also, we
introduce the notion of nonholonomic Jacobi field and provide a nonholonomic
Jacobi equation. In the second part, which is more applied, we use the nonholonomic
exponential map to characterize the exact discrete trajectory of
nonholonomic systems and propose a numerical method
that is able to generate the exact trajectory. Finally, we apply the nonholonomic exponential map to
construct an exact discrete Lagrangian function for discrete contact systems.
Fecha: 27 de Julio, 17:00 (hora peninsular)
ID de Reunión: 876 3984 8330