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ANALYTICAL MECHANICS

CODE 107033
ACADEMIC YEAR 2021/2022
CREDITS
  • 6 cfu during the 2nd year of 8758 FISICA (L-30) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/07
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 2° Semester
    TEACHING MATERIALS AULAWEB

    OVERVIEW

    During these lectures, the student is introduced to the Lagrangian and Hamiltonian formulation of the classical mechanics.

    Furthermore, the lectures contains also some elements of the theory of stability for dynamical systems, variational principles and Hamilton-Jacobi equation.

     

    AIMS AND CONTENT

    LEARNING OUTCOMES

    The principal aim of the course is to give to the student the knoweledge of Lagrangian an Hamiltonian mechanics.

    Furthermore, the student is beleived to acquire the ability of resolving typical probelms of classical mechanics by means of the theoretical instruments furnished by the Lagrangian and Hamiltonian mechanics.

    AIMS AND LEARNING OUTCOMES

    At the end of the learing path the student will be able to:

    - describe the foundations of the Lagrangian and Hamiltonian formulation of classical mechanics

    - describe the dynamics of classical systems by means of the Euler-Lagrange equation

    - find the equilibrium configurations of Lagrangian systems

    - analyze the stability of the equilibrium configurations of these systems

    - formulate the equation of motion in the case of Hamiltonian mechanics

    - know and use the canonical transforamtions

    - know some advanced techniques to solve some motion equations like those furnished by the Hamilton-Jacobi equation

    - characterize the studied equation of motion by means of some variational principles

    TEACHING METHODS

    The course are organized in lectures given by the teachers where the theoretical part it will be presented and where its application to the resulutions of some exercises will be discussed.

    SYLLABUS/CONTENT

    Introduction and some basic concepts

    • Spacetime of the classical mechanics

    Analytical mechanics of holonomic systems

    • Holonomic systems and ideal constraints
    • Euler-Lagrange equations
    • Lagrange equation and balance equations
    • Integrals of motion in the Lagrangian formalism

    Introduction to stability of dynamical systems

    • Equilibrium solution, critical points and their stability
    • Small oscillations for a mechanical systems

    Hamiltonian mechanics

    • Legendre transformation and Hamilton's equations
    • Poisson brackets
    • Canonical transformations and generating functions
    • Transformation law for the Hamiltonian 
    • Hamilton-Jacobi equation

    Variational principles

    • Lagrangian case and Hamiltonian case
    • Canonical transformations and covariance of the action functional

     

    RECOMMENDED READING/BIBLIOGRAPHY

    The notes of the course will be made available within aul@web.

    Further deeper suggested readings:

    1) H. Goldstein, C. Poole, J. Safko, “Classical Mechanics”, 3rd edn. Addison-Wesley, San Francisco, (2002).

    2) V. I. Arnold “Metodi Matematici della Meccanica Classica” Editori Riuniti University Press, (2010).

    TEACHERS AND EXAM BOARD

    Exam Board

    NICOLA PINAMONTI (President)

    PIERRE OLIVIER MARTINETTI

    MARCO BENINI (President Substitute)

    LESSONS

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    EXAMS

    EXAM DESCRIPTION

    The exam is usually formed by a written and by an oral part.

    ASSESSMENT METHODS

    The written exams verifies the ability of the student to solve some exercises by means of the tecniques studied during the lectures.

    The oral part is about the teoretical arguments presented during the lectures.

    Exam schedule

    Date Time Location Type Notes
    08/06/2022 09:00 GENOVA Scritto per Fisica con accettazione online
    12/07/2022 09:00 GENOVA Scritto per Fisica con accettazione online
    07/09/2022 09:00 GENOVA Scritto per Fisica con accettazione online