Unit RATIONAL MECHANICS
- Course
- Civil and environmental engineering
- Study-unit Code
- 70003308
- Curriculum
- In all curricula
- Teacher
- Giuseppe Saccomandi
- Teachers
-
- Giuseppe Saccomandi
- Hours
- 64 ore - Giuseppe Saccomandi
- CFU
- 8
- Course Regulation
- Coorte 2021
- Offered
- 2022/23
- 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
- Classical Mechanics of Points and Rigid-Bodies with special emphasise on Statics
- Reference texts
- Biscari, P., Ruggeri, T., Saccomandi, G., & Vianello, M. (2015). Meccanica razionale (Vol. 93). Springer.
- Educational objectives
- The ability to solve problems about the statics of free and constrained systems.
- Prerequisites
- Calculus and general Physics.
- Teaching methods
- Classical
- Other information
- None
- Learning verification modality
- Written and oral examination
- Extended program
- Geometry, trigonometry and vector algebra: vector algebra in three dimensions using different bases, length, addition and multiplication of vectors, inner product and cross product. The properties of the inner product and the vector product, geometric and physical interpretations, rules of differentiation for vector functions, differentiation of coordinates and basis vectors in different coordinate systems. Curves, area elements, volume elements.
Applications of statics and geometry: force, torque.
The kinematics of particles in different coordinate systems, cartesian-, normal and tangential- as well as polar coordinates.
The dynamics of particles: force, linear momentum, impulse, torque, angular momentum, angular impulse, Newton's laws.
Particle systems, center of mass, Euler's law for the movement of the the center of mass. Mass flows, the rocket equation.
Work and energy. Energy relations. Gradient.
Accelerated reference frames.
The development of the mechanics. Kepler's laws. Short introduction to oscillatory motion.
Models for the motion of objects with applications.
Introduction to Lagrangian Mechanics. Stability and Oscillations