Mathematical Physics

Code: -
|
MAT/07
The course introduces the fundamental principles of classical mechanics and their applications in a physical-mathematical key to model, analyse and solve problems related to engineering. The course aims at providing students with basic notions of vector calculus, kinematics, geometry of masses and statics of systems of material points, rigid bodies, and composite systems.

Lesson hours:

48

Practice hours:

-

Propaedeuticities:

Basic mathematics and analysis, Linear algebra and Geometry

Credits:

6

Types of examinations:

Written and Oral test

Teacher:

-

Objectives:

  • Analyse and translate a concrete problem of mechanics into an abstract model
  • Identify the geometric-material characterization of a mechanical system
  • Describe the kinematics of an arbitrary holonomically constrained system with special focus on rigid motions
  • Illustrate kinematically the constrains and the related exerted actions imposed on a system
  • Individuate the equilibrium state of a rigid system and determine its internal and external constraint reactions

Contents:

[2 CFU] Overview of vector and tensor algebra. Equivalent vector fields and properties of moments. Geometry of masses. Kinematics of rigid systems. Axis of motion and Mozzi’s theorem. Plane rigid motions with applications. Relative kinematics. Constraints. Degree of freedom and Lagrangian coordinates. Displacements (finite, elementary, possible and virtual). Degree of lability. Kinematic analysis of constraints.

[2 CFU] Newton’s model and basics of particle mechanics. Work. Potential and energy. Constraint forces. Laws of friction. Forces by ideal constraints; smooth constraints are ideal. Dynamics Equations for a general material system and related theorems. Applications to rigid bodies and equations of motion for material systems with ideal (in particular, smooth) constraints.

[2 CFU] Statics Equations. Calculation of constraint forces, solving plane structures subject to distributed or concentrated loads. Calculation of stresses in trusses, method of knots and Ritter’s method of sections. Principle of virtual works and its applications. Basics of mechanics of continuous systems.

Teaching materials:

To be completed.