Enrollment year
2019/2020
Academic discipline
MAT/07 (MATHEMATICAL PHYSICS)
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Curriculum
PERCORSO COMUNE
Period
2nd semester (01/03/2021 - 11/06/2021)
Lesson hours
84 lesson hours
Activity type
WRITTEN AND ORAL TEST
Prerequisites
Analysis 1, Analysis 2, Linear Algebra.
Learning outcomes
The aim of the course is to present the basic mathematical models of classical mechanics, in their theoretical aspects and in their applications.
Course contents
Kinematics of a point.
Dynamics: fundamental principles.
The motion of a free particle.
Constraints.
Multi particles systems.
Rigid systems.
Cardinal equations of dynamics.
Lagrange's equations.
Some classical problems: the problem of two bodies.
Equilibrium and stability.
Hamilton's principle.
Hamilton's equations.
Canonical tranformations. Poisson brackets.
Extended summary
Kinematics of a point. Frenet's frame.
Constraints and their classification.
The motion of a free particle.
Lagrangian coordinates.
Dynamics: the fundamental principles of mechanics.
Work and energy. Conervatives forces.
The motion of a point under constraint.
Discrete systems. Cardinal equations of dynamics. Non dissipative constraints.
Lagrange's equations. Lagrange's equations for conservative systems. Conservations laws.
One-dimensional motions. Qualitative analysis.
Some classical problems: the problem of two bodies. Keplero's equations.
Rigid body: Euler's angles. Angular velocity. Relative motions.
Rigid body dynamics: inertia ellipsoid. Euler's equations. Lagrange's gyroscope.
Equilibrium and stability: Lagrange-Dirichlet theorem. Instability criteria. Small oscillations.
Variational principles of mechanics: Hamilton's principle.
The Hamiltonian function (via Legendre transformation). Hamilton's equations.
Canonical tranformations. Poisson brackets.
Teaching methods
Lectures and exercises.
Reccomended or required readings
1.Fasano A., Marmi S.,: "Meccanica Analitica", Bollati Boringhieri.
2.Goldstein H., Poole C., Safko J.: "Meccanica Classica", Zanichelli.
3.Gantmacher F.R.: "Lezioni di Meccanica Analitica", Editori Riuniti.
4.Lanczos C., : "The variational principles of Mechanics, Dover.
Assessment methods
Written and oral examination.
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