First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
ASTRONOMY
Course unit
ANALYTICAL MECHANICS
SC05105660, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2016/17

Information on the course unit
Degree course First cycle degree in
ASTRONOMY
SC1160, Degree course structure A.Y. 2008/09, A.Y. 2017/18
N0
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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/2017/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

Mode of delivery (when and how)
Period Second semester
Year 2nd Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Lecture 7.0 56 119.0 No turn

Calendar
Start of activities 26/02/2018
End of activities 01/06/2018

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 ODE describing a mechanical system.
Ability to solve a system of ODE 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 exam 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:
- ability to recognize the type of mechanical system under study
- ability to choose and apply the right solutions tools (theorems, procedures) for the system of ODE
- ability to organize a clear written exposition of a topic of the program
- ability to reproduce a proof of a theorem presented during the lesson
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), moodle interaction with students, use of tablet and other devices
Additional notes about suggested reading: On the web page lecture notes of the course are available written by the teacher.
Texts of the previous written exam are also available on the teacher web page
Textbooks (and optional supplementary readings)