
Course unit
ANALYTICAL MECHANICS
SC05105660, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2018/19
Lecturers
No lecturer assigned to this course unit
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
MAT/07 
Mathematical Physics 
7.0 
Course unit organization
Period 
Second semester 
Year 
2nd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
7.0 
56 
119.0 
No turn 
Prerequisites:

Physics notions: reference frame, kinematics and dynamics of a material point, kinetic and potential energy, conservative and non conservative forces.
Mathematical preliminaries: differential calculus in several variables, integral calculus in one variable, line integrals, differential forms, manifolds, linear and non linear ordinary differential equations, phase portrait.
Algebric and geometric notions: euclidean vector spaces, matrix and linear transformations, eigenvectors and eigenvalues, determinant 
Target skills and knowledge:

Knowledge of the models of material point, rigid body, system of material points, constrained system. Ability to deal with the problem of writing the ordinary differential equations describing a mechanical system. Ability to solve a system of ordinary differential equations using qualitative methods and theorems (equilibria, stability analysis, energy methods, linearization, variational formulation of the equations, unicity). 
Examination methods:

Written exam consisting in the solution of exercises and answering of open questions about selected topics of the program. The final examination can be passed also with two written exams during the term (one concerning the first half of the programe and the second concerning the second part of the program). 
Assessment criteria:

The assessment of the result of the written examination will be based on the following criteria:
1) ability to recognize the type of mechanical system under study
2) ability to identify the correct way to determine the equation of motion;
3) ability to choose and apply the right solutions tools (theorems, procedures) for the system of ordinary differential equations;
4) ability to organize a clear written exposition of a topic of the program;
5) ability to reproduce a proof of a theorem presented during the lectures. 
Course unit contents:

Study of phase portrait for autonomous sysyems. Two body problem. Theory of stability of equilibria. Dynamics of a system of material points. Kinematics of rigid systems. Angular velocity. Non inertial frames. Apparent forces. Tidal forces. Cardinal equations (balance of momentum and angular momentum). Constrained systems. Workless constraints. Lagrange equations. Routh reduced equations. Noether Theorem. Linearization of Lagrange equations. Small oscillations. Geodesic motions. Hamilton variational principle. Rigid body dynamics. Euler equation and solutions. Hamilton equations. HamiltonHelmholtz variational principle. Poisson brackets. 
Planned learning activities and teaching methods:

Classroom lessons, solution of exercises, tutoring of students, handhouts of lessons and other material (previous written exam texts), web interaction with students, use of tablet and other devices. Lectures are given in Italian. 
Additional notes about suggested reading:

Lecture notes of the course by the teacher are available through the website of the course on the elearning platform of the Department of Mathematics "T. Levi Civita" (https://elearning.unipd.it/math/). Texts and solutions of the previous written exam are available through the website of the teacher (http://www.math.unipd.it/~favretti/didattica.html). 
Textbooks (and optional supplementary readings) 

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)

