Tesis

Tesis

LECTURA DE TESIS -- Geometric and Numerical Analysis of Nonholonomic Systems

Ponente:  Alexandre Anahory Simoes, ICMAT-UAM // Advisors: David Martín de Diego, ICMAT-CSIC, y Juan Carlos Marrero, Universidad de La Laguna ()
Fecha:  viernes 26 de noviembre de 2021 - 18:30
Lugar:  Aula Naranja (ICMAT) y online - us06web.zoom.us/j/85923463760?pwd=TEpRNm9CcHEyN3FUenE5WStSN0NlZz09 (ID: 859 2346 3760; passcode: 673246)

Resumen:

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.

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