First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
ASTRONOMY
Course unit
ANALYTICAL MECHANICS
SC05105660, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course First cycle degree in
ASTRONOMY
SC1160, Degree course structure A.Y. 2008/09, A.Y. 2018/19
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Number of ECTS credits allocated 7.0
Type of assessment Mark
Course unit English denomination ANALYTICAL MECHANICS
Website of the academic structure http://astronomia.scienze.unipd.it/2018/laurea
Department of reference Department of Physics and Astronomy
Mandatory attendance
Language of instruction Italian
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge MARCO FAVRETTI MAT/07

ECTS: details
Type Scientific-Disciplinary 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

Calendar
Start of activities 25/02/2019
End of activities 14/06/2019

Examination board
Examination board not defined

Syllabus
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. Hamilton-Helmholtz 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 e-learning 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
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • One Note (digital ink)
  • Latex
  • Mathematica