First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
Course unit
IN02105695, 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
IN0506, Degree course structure A.Y. 2011/12, A.Y. 2017/18
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Degree course track FORMATIVO [001PD]
Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination ANALYTICAL MECHANICS
Department of reference Department of Industrial Engineering
E-Learning website
Mandatory attendance No
Language of instruction Italian
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

Teacher in charge ADRIANO MONTANARO MAT/07

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/07 Mathematical Physics 9.0

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

Organisation of didactics
Type of hours Credits Hours of
Hours of
Individual study
Lecture 9.0 72 153.0 No turn

Start of activities 25/09/2017
End of activities 19/01/2018

Examination board
Board From To Members of the board
9 A.A. 2016/17 01/10/2016 30/11/2017 MONTANARO ADRIANO (Presidente)
FAVRETTI MARCO (Membro Effettivo)

Prerequisites: The course contents (1) MATHEMATICAL ANALYSIS 1
Target skills and knowledge: Basic training in classical Rational Mechanics and in Mechanics of Lagrangian systems.
Knowledege of some basic facts in the dynamics of rigid bodies with applications of interest in mechanical engineering.
Examination methods: Traditional
Assessment criteria: Written examination and oral examination
Course unit contents: Classical Rational Mechanics, Lagrangian Mechanics, dynamics of rigid bodies. In details:
Vectors recalls. Cartesian components; scalar, vectorial and mixed product; double vectorial product.
Vector fields. Torsors; central axis; sum of torsors.
Applied vector systems. Polar moment, axial moment; equivalence of two systems of applied vectors; elementary operations and reducibility; reduction of an applied vector systems; plane vector systems; parallel vector systems.
Point kinematics. Vector velocity and acceleration in Frenet-Serret (intrinsic) frame; elementary displacement.
Kinematics of rigid systems. Rigid displacements and rigid motions, cartesian equations of a rigid motion, expression of angular velocity; Poisson's formulas; velocity, acceleration and elementary displacement fields; elementary rigid motions; plane and spherical rigid motions; motion acts and their compositions.
Relative kinematics and applications to rigid motions. Velocity composition theorem; Coriolis theorem, geometric description of a rigid motion as mutual rolling of two surfaces; polar trajectories in plane rigid motions; precessions.
Mass geometry. Mass; mass center of a discrete or continuous system; inertial momentum; Huygens-Steiner theorem; inertial tensor and ellipsoid of inertia; gyroscope.
Mass kinematics. Linear momentum; angular momentum; kinetic energy; motion relative to the center of mass; Koenig theorem; expressions of kinetic energy and angular momentum for a rigid body.
Kinematics of constrained systems. Geometric, kinematic, bilateral, unilateral constraints; holonomic systems; possible and virtual displacements.
Forces and Work. Positional and conservative force fields; elementary and effective work; work along a finite path for positional and conservative forces; work of a force system; expression of work of a force system acting on a rigid body; possible and virtual works in holonomic systems.
Principles of mechanics. Inertial frames and Newton laws for discrete systems; postulate of reaction forces; cardinal equations of dynamics for physical systems formed by concentrated masses and rigid bodies with internal and external constraints; kinetic energy theorem and integral of energy; non-inertial frames and apparent forces.
Statics of a system of material points. Equilibrium positions; principle of virtual works for a system of material points; equilibrium in a non-inertial frame.
Statics of the rigid body. Equilibrium configurations, cardinal equations of statics and principle of virtual works for a rigid body.
Lagrangian Mechanics for holonomic systems. General equation of dynamics; free coordinates; Lagrange equations in the first and second form; equilibrium stability and small oscillations in the neighbourhood of a stable equilibrium configuration; normal modes; stability criterion of Lagrange-Dirichlet and instability criterion of Lyapounov.
Dynamics of spherical rigid motions. Eulero's equations; gyroscopic phenomena, study of the Poinsot motions and their geometric description.
Applications of the theory to discrete systems and rigid bodies. Comparison of simple pendulum and compound pendulum; static-dynamic comparison of reaction forces on the rotation axis of a rigid body.
Planned learning activities and teaching methods: Learning activities: regular exercises assigned for home, quiz/test online on the page Moodle of the course, classroom exercises to check on the degree of understanding of the arguments.

Teaching methods: lectures; analysis of the solutions to the exercises in the classroom proposals.
Additional notes about suggested reading: Moodle page of the course where resources are accessible as the daily diary of the lessons, exercises, the examination carried out with solutions, slides of individual lessons.
Textbooks (and optional supplementary readings)
  • A. MONTANARO, Meccanica Razionale - Teoria. Padova: Librerie Progetto, 2017. Nuova edizione Cerca nel catalogo
  • A. MONTANARO, Meccanica Razionale - Esercizi. Padova: Librerie Progetto, 2017. Nuova edizione Cerca nel catalogo