COMPLEMENTS OF RATIONAL MECHANICS
Academic year and teacher
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- ARIANNA PASSERINI
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- MAT/07
Training objectives
- Aim of the Course is to implement the skills in applications by further theoretical tools. The notion of Stability deserves a huge relevance in Mechanics and Fluid Dynamics. For its several applications (vibrations, software, heat transport), the knowledge of the full path, from theory to practice uses, is a meaningful tool to get an overview of physical phenomena and solve the problems
Prerequisites
- Basic notions in Ordinary Differential Equations, Banach Spaces (Hilbert Spaces, in particular) and Fluid Dynamics. See the courses Complementi di Analisi and Termofluidodinamica Numerica
Course programme
- Stability definition for critical points. Lyapunov's Theorem. Mechanical Energy as Lyapunov function for olonomic systems (6 hours). Stability of solutions of Euler equations for the rigid body (12 hours). Small oscillations. Linearization. Bifurcations (16 hours). The heat equation and the decay rate. Dissipative systems: energy stability for Navier-Stokes equations (10 hours). Critical Rayleigh number for convection (16 hours).
Didactic methods
- Lectures in the classroom.
Learning assessment procedures
- Oral test
Reference texts
- Galdi G.P., An Introduction to the Mathematical Theory of the Navier-Stokes Equations, I-II, Springer.
Straughan B., The Energy Method, Stability and Nonlinear Convection
Lecture Notes