60/60/143 - ANALYTIC MECHANICS
Academic Year 2022/2023
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SALVATORE MIGNEMI (Tit.)
- Teaching style
- Lingua Insegnamento
|[60/60] PHYSICS||[60/00 - Ord. 2012] PERCORSO COMUNE||8||64|
Learn the fundaments of analytical mechanics needed for
affording the study of advanced physics courses.
Calculus, Geometry, Physics I
Vectorial spaces. Linear applications. Geometry of curves.
Newton laws. Conservative forces and potentials. Mechanics of particles. Mechanics of systems. Poisson formulae and relative kinematics. Apparent forces.
Constraints. D'Alembert principle. Lagrange equations. Generalized potentials. Hamilton principle. Elements of variational calculus. Conservation theorems and symmetry. Energy conservation.
Central forces. Equations of motion and first integrals. Classifications of orbits. Solutions of Kepler problem. Runge-Lenz vector.
Definition of rigid body. Rotations. Euler angles. Matrices of inertia. Kinetic energy of rigid bodies. Euler equations. Free motion of a rigid body. Motion of a rotator in a gravitational field.
Stability of equilibrium. Harmonic oscillator. Eigenfrequencies. Normal coordinates. Forced oscillator.
Legendre transformations. Hamilton equations. Conservation theorems. Modified Hamilton principle. Canonical transformations. Poisson brackets and their properties. Infinitesimal contact transformations. Hamilton-Jacobi equation. Hamilton principal and characteristiic functions. Separation of variables. Two-center problem.
Dynamical systems. Critical points. Linearization. Examples.
64 hours of lectures, of which 16 of practice Because of the epidemiological situation it is possible that classes will be available online.
Verification of learning
Written and oral examination
Goldstein, Classical mechanics
Some exam tests with solutions are avilable on the site