Mechanical Engineering for the Green Transition

Introduction to the course: particle kinematics, moving frame, plane motion in polar coordinates, angular velocity, Poisson formulas. Rigid motion: theory and exercises. Euler's theorem. Center of instantaneous rotation, scalar invariant, classification of constraints, free coordinates and degrees of freedom, disk rolling on a fixed guide. Theory: relative motions. Galileo's theorem (composition of velocities), Coriolis's theorem (composition of accelerations), Einstein's elevator. Principles of Mechanics. Examples of forces (e.g., positional, dissipative, etc., active and reactive forces), Coulomb-Morin law, apparent forces. Mechanical quantities (momentum, momentum, kinetic energy) for systems of particle points. Center of gravity, theorem of motion of the center of gravity. First Cardinal Equation, Second Cardinal Equation. Work, potential, and power: exact differentials. Kinetic Energy Theorem, Work Theorem. Conservation of Mechanical Energy, Momentum, and Angular Momentum: First Integrals. Rigid Body: Inertia Tensor, Principal Axes of Inertia, Steiner's Theorem. Momentum and Angular Momentum for the RC. Kinetic Energy and Power for the RC. Constraints and Reactions. The Case of Rolling Friction and Pure Rolling. Cardinal Equations and First Integrals for Constrained Systems. Introduction to Analytical Mechanics. Symbolic Equation of Dynamics. Analytical Statics: The Principle of Virtual Work. Toward the Lagrangian Formulation of Mechanics: From the Symbolic Equation to Lagrange's Equations in Non-Conservative Form. Lagrangian and Lagrange Equations. Conservation Theorems in the Lagrangian Formalism. Noether's Theorem: Symmetries and First Integrals. Qualitative analysis of one-dimensional conservative systems, equilibrium stability of conservative holonomic systems, Lyapunov and Dirichlet-Lagrange theorems. Theory of small oscillations, Lagrangian of small oscillations, stability through study of the eigenvalues ​​of the relevant dynamical systems.

Knowledge of Mathematical Analysis I-Mathematical Analysis II Geometry I-Physics I.

E, Cirillo Notes from the Lessons of Rational Mechanics - Ed. CompoMat 2018 Stefano Turzi Notes on rational mechanics provided in the relevant classroom RATIONAL MECHANICS 2025

Recommended although not mandatory given the nature of the course which requires constant interaction between theory and applications.

The exam consists of a written test concerning the topics covered in the course and structured in such a way as to verify the knowledge acquired in order to solve problems. There are also theoretical questions aimed at verifying the mastery of the acquired theoretical knowledge.

Lectures and exercises.