


Politecnico di Torino  
Academic Year 2016/17  
02BORNE Theoretical mechanics 

Master of sciencelevel of the Bologna process in Mechanical Engineering  Torino 





Subject fundamentals
The course is devoted to the modeling by means of a set of ordinary differential equations, of dynamic systems in the framework of classical mechanics. The derivation of evolution equations is based on the background developed from Newtonian mechanics (Lagrange and Hamilton equations for holonomic systems with ideal constraints). Once the evolution equations are obtained mathematical problems can be considered by adding initial conditions. A qualitative and quantitative analysis of specific mechanical problems is provided by using analytic methods or by means of the softwares Matlab and Dynamics Solver to obtain useful simulations. Finally, Liapunov stability as well as bifurcations and chaotic behaviors of dynamical systems are introduced in the course and analysed by means of suitable examples.

Expected learning outcomes
Attending this course, students learn to deduce in an analytic way the time evolution equations of discrete mechanical systems (i.e. they can obtain the mathematical model of the considered dynamic system). By using the above equations they can determine all the stationary states with their stability and they can estimate the dynamic behavior of the system by means of analytic methods or by using suitable simulations adequately interpreted.

Prerequisites / Assumed knowledge
The bases of Newtonian mechanics and the theory of ordinary differential equations represent the requested background for attending this course. They are usually teached in the previous basic courses.

