ID:
500474
Duration (hours):
60
CFU:
6
SSD:
FISICA MATEMATICA
Year:
2025
Overview
Date/time interval
Primo Semestre (29/09/2025 - 16/01/2026)
Syllabus
Course Objectives
The course aims at giving an overwiev of classical mechanics to show that an adequate mathematical formulation can give a deep insight into the problems of this discipline (inertia properties, lagrangian dynamics, stability of equilibrium in holonomic systems, normal modes, Poinsot motion, Largange top).
Course Prerequisites
Notions given in basic courses in Mathematical Analysis and Calculus (Analisi Matematica), Linear Algebra, Geometry (Geometria e Algebra), and Physics (Fisica).
Teaching Methods
The course consist of theoretical lectures, and problem solving / exercises lectures ('esercitazioni'), tightly correlated with one another.
Theoretical lectures aim at giving basic concepts and results, always with some reference examples. Examples and exercises aim at developing computational skills and reasoning capabilities useful to tackle complex problems.
Lectures and exercise sessions at the blackboard, if possible; on-screen lessons by means of a tablet will be the alternative.
Lectures (hours/year in lecture theatre): 22.5
Practical class (hours/year in lecture theatre): 37.5
Practicals / Workshops (hours/year in lecture theatre): 0
Theoretical lectures aim at giving basic concepts and results, always with some reference examples. Examples and exercises aim at developing computational skills and reasoning capabilities useful to tackle complex problems.
Lectures and exercise sessions at the blackboard, if possible; on-screen lessons by means of a tablet will be the alternative.
Lectures (hours/year in lecture theatre): 22.5
Practical class (hours/year in lecture theatre): 37.5
Practicals / Workshops (hours/year in lecture theatre): 0
Assessment Methods
Written test and oral test. The written test will allow assessing the skills acquired by the student in order to tackle problems on the content of the course. Questions and problems will be graduated in difficulty to determine the real level of knowledge and skills acquired by the student.
The teacher may decide to propose the sudents who passed the written test (mark greater than or equal to 18/30) either the verbalisation of the mark obtained in the written test or an oral exam. In any casde, student may required to undergo an oral test, provided they obtained in the written test a mark greater than or equal to 18/30.
If the mark of the written part is greater tahn 26/30, if no oral test is required (by the student or by the teacher), the final mark will be 26/30. In the oral test focus will be on assessing the level of theoretical knowledge acquired during the course, the clarity with which such knowledge is displayed. and the capability of applying such knowledge.
The final mark is the result of global width and depth of knowledge, as well as of the clarity of speech and of skills shown in solving problems. Such fina mark will not necessarily be the arithmetical mean of the mark obtained in the oral and written tests.
The teacher may decide to propose the sudents who passed the written test (mark greater than or equal to 18/30) either the verbalisation of the mark obtained in the written test or an oral exam. In any casde, student may required to undergo an oral test, provided they obtained in the written test a mark greater than or equal to 18/30.
If the mark of the written part is greater tahn 26/30, if no oral test is required (by the student or by the teacher), the final mark will be 26/30. In the oral test focus will be on assessing the level of theoretical knowledge acquired during the course, the clarity with which such knowledge is displayed. and the capability of applying such knowledge.
The final mark is the result of global width and depth of knowledge, as well as of the clarity of speech and of skills shown in solving problems. Such fina mark will not necessarily be the arithmetical mean of the mark obtained in the oral and written tests.
Texts
F. Bisi, R. Rosso: Introduzione alla meccanica teorica (available on www.amazon.it).
P. Biscari, C. Poggi, E.G. Virga, Mechanics Notebook (Liguori, Napoli).
P. Biscari, C. Poggi, E.G. Virga, Mechanics Notebook (Liguori, Napoli).
Contents
Vector and tensor algebra
Scalar and vector product; mixed product and repeated vector product; Diadics; symmetric tensors: spectral theorem. Skew-symmetric tensors: spin axis. Orthogonal tensors. Systems of vectors
Relative and rigid-body kinematics
Poisson formulae; Time derivatives of vectors in different frames. Basic formulae in relative kinematics. Fundamental formula in rigid kinematics.
General kinematics
Center of mass of a system of material points; Momentum, moment of momentum, and kinetic energy. Transport theorem for moment of momentum. König's theorem.
Inertia tensor
Definition and main properties of the inertia tensor. Moments of inertia. Huygens-Steiner theorem. Theorem of perpendicular axes. Composition theorem. Material symmetry.
General dynamics
Balance equations. Kinetic energy theorem. Conservation laws. Power expanded in a rigid motion.
Lagrangian dynamics
Lagrange's equations of motion
Stability of motion
Stability of motion according to Ljapunov. Dirichlet-Lagrange theorem. First Ljapunov's instability criterion.
Normal modes
Linearization of Lagrange's equations; normal co-ordinates. Oscillating, linear, and hyperbolic normal modes.
Rigid-body dynamics, Lagrangian top, stability.
(see also https://elearning.unipv.it/course/view.php?id=2889)
Scalar and vector product; mixed product and repeated vector product; Diadics; symmetric tensors: spectral theorem. Skew-symmetric tensors: spin axis. Orthogonal tensors. Systems of vectors
Relative and rigid-body kinematics
Poisson formulae; Time derivatives of vectors in different frames. Basic formulae in relative kinematics. Fundamental formula in rigid kinematics.
General kinematics
Center of mass of a system of material points; Momentum, moment of momentum, and kinetic energy. Transport theorem for moment of momentum. König's theorem.
Inertia tensor
Definition and main properties of the inertia tensor. Moments of inertia. Huygens-Steiner theorem. Theorem of perpendicular axes. Composition theorem. Material symmetry.
General dynamics
Balance equations. Kinetic energy theorem. Conservation laws. Power expanded in a rigid motion.
Lagrangian dynamics
Lagrange's equations of motion
Stability of motion
Stability of motion according to Ljapunov. Dirichlet-Lagrange theorem. First Ljapunov's instability criterion.
Normal modes
Linearization of Lagrange's equations; normal co-ordinates. Oscillating, linear, and hyperbolic normal modes.
Rigid-body dynamics, Lagrangian top, stability.
(see also https://elearning.unipv.it/course/view.php?id=2889)
Course Language
Italian
More information
In agreement with project 'didattica innovativa' students with special needs may be offered office hours in the evening or the availability of the notes prepared by the instructor.
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