Unit APPLIED MECHANICS
- Course
- Industrial engineering
- Study-unit Code
- 70003306
- Curriculum
- In all curricula
- Teacher
- Luca Valentini
- Teachers
-
- Luca Valentini
- Hours
- 54 ore - Luca Valentini
- CFU
- 6
- Course Regulation
- Coorte 2020
- Offered
- 2021/22
- Learning activities
- Base
- Area
- Matematica, informatica e statistica
- Academic discipline
- MAT/07
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- In this course the concepts and methods of Classical Mechanics will be presented. In particular, reference will be made to the mechanics of the material point, the mechanics of constrained point systems, the mechanics of the rigid body and the Lagrangian mechanics. In the first part of the course we will study the systems of points and rigid bodies through the use of cardinal equations and the kinetic energy equation. In the second part of the course the principles of Analytical Mechanics will be introduced with reference to the study of stability and the equilibrium of a mechanical system.
- Reference texts
- Slides of the course.
- Educational objectives
- The knowledge the mechanical models at a finite number of degrees of freedom, the methods to analyze their mechanical behavior under the action of assigned solicitations, the determination of the constraints and the corresponding constraint reactions and the determination of the actions necessary to have assigned mechanical behaviors.
- Prerequisites
- The student should have the tools of: Mathematical Analysis, Geometry and having studied the part of Mechanics contained in the course of Physics.
- Teaching methods
- The course is 5 CFU and is divided into lessons that are generally divided into:
Frontal lesson that illustrates the new theoretical concepts. This will be followed by a part of the study that illustrates the previous lesson with solved exercises A third party requires the performance of exercises assigned in the classroom in such a way that the student can assess his learning level. - Learning verification modality
- Written exam with oral examination. The interview will focus on the discussion of the paper and some questions on the theory part.
- Extended program
- 1. Definition of vector, scalar product, vector product;
2. Review of matrix algebra, Tensor product;
3. The harmonic oscillator, Kinematics of the material point;
4. Rigid motion, Angular velocity Poisson formulas, Analysis of the rigid motion
5. Plane motion: angular velocity, Plane motion: center of instantaneous rotation (CIR)
6. Kinematic classification of the constraints, point systems, free coordinates, degrees of freedom, kinematic exercises of the rigid body (RB);
7. Relative kinematics Galileo's theorem, related kinematics Coriolis theorem, Principles of material point mechanics, Examples of forces, friction, dynamics of the material point, 1st cardinal equation, 2nd cardinal equation;
8. Reduction of force systems, Work, potential, Kinetic energy theorem, Conservation of mechanical energy, Prime integrals;
9. Properties of the center of gravity, Moment of inertia, Moments of inertia with respect to parallel axes, Moments of inertia with respect to concurrent axes, Matrix of inertia, Axes and main moments of inertia;
10. Momentum flow and angular momentum for the RB, Kinetic energy and power for the RB, Plane case, Examples of supportive reactions, RB dynamics exercises;
11. Statics Cardinal equations, Statics of wires, Static exercises;
12. Introduction to Analytical Mechanics, Relationship and Symbolic Equation of Dynamics, Static Principle of Virtual Works (PLV), Statics of Holonomic Systems, Stationarity of Potential, Analytical Static Exercises;
13. Lagrange equations, Lagrange equations for a conservative system, First kinetic and integral moments, Generalized integral of energy, Exercises solved with Lagrange eqs;
14. Stability of the equilibrium of conservative holonomic systems, small oscillations, stability exercises.