The course provides mathematical methods for describing mechanical systems. In particular the motion of systems with many degrees of freedom is studied and the properties of the center-of-mass of continuous systems are analyzed. Rigid body, moments of inertia and specific rigid body motions are analyzed in details.
The analysis of the behavior of a machanical (but also electrical) system needs the recourse to mathematical methods. It is the purpouse of this course providing the mathematical tools which are relevant to the study and to the description of mechanical systems. The course starts from the most simple mechanical system, the so called mass-point model, and proceeds with systems having many degrees of freedom with a view to arriving at the rigid body which is examined in datails. Precisely the course provides a technical approach to moments of inertia and analyzes specific rigid body motions. The last chapter is dedicated to the study of the equilibrium of a wire under various hypothesis on the distribuited force. It is remarkable that all the machanical situations analized in the course, although all the systems are continuous systems, are governed by ordinary differential equations.
The course consists of lectures and exercises
Elements of vector calculus. Kinematics and relative kinematics. Dynamics and statics of material points. Cardinal equations. Center of mass. Conservation laws. Energy theorem. Mechanics of the rigid body. Moments of inertia. Rigid body with a fixed axis, a fixed point, without contraints. Statics of wires
F. Bampi, C. Zordan, Lezioni di Meccanica Razionale, Ecig, Genova, 1998.
F. Bampi, M. Benati, A. Morro, Problemi di Meccanica Razionale, Ecig, Genova, 1992.
Ricevimento: By appointment: call the 010-353.6000 to schedule an appointment
FRANCO BAMPI (President)
ROBERTO CIANCI
CLAUDIO CARMELI (President Substitute)
MATHEMATICAL PHYSICS
The examination consists of an oral test
The assessment of what a student has learned is realized through an oral examination which consists in two questions regarding the content of the whole course. The students are also provided with the list of all the questions (about fifty) that will be the subject of the oral examination.
