
MODELING AND SIMULATION OF MECHANICAL SYSTEMS
Prerequisites:

Applied mechanics
Mechanical vibrations
Mechanical and thermal measurement systems 
Examination methods:

The exam includes two mandatory activities: an individual assignment and a written exam. The assignment contributes 15/30 of the final grade while the written exam contributes 15/30. The assignment consists in carrying out a multibody modelling and simulation project and presenting such project. The written exam consists in answering three open questions in about 2 hours; the use of lecture notes and/or textbooks is not permitted. The exam may be carried out either in Italian or in English, according to the studentâ€™s preference. 
Course unit contents:

Kinematics of multibody systems: translation and rotation matrices for threedimensional systems, Rodrigues formula, conventions for the orientation of bodies in space (with three and four parameters), singular points, angular velocities expressed in ground frame and moving frame, main constraints for multibody systems, Grubler equation for threedimensional systems, problems related to redundant constraints, position and velocity initial analysis, examples in Maple and applications in Adams.
Dynamics of multibody systems: Lagrange's equations for systems with constraints and resulting DAE system, different conventions for the inertia tensor, first order reduction of the equations of motion, DAE index, stabilization of constraint equations using the Baumgarte method, from DAE to ODE using the coordinate partitioning method, automatic partitioning using the LU decomposition, different definitions of 'stiff' systems, 'GearGuptaLeimkuhler' and 'HillerAnantharaman' formulations for the reduction of the DAE index, equilibria, examples in Maple and applications in Adams.
Linearization of multibody systems: computation of the state matrices A,B,C,D and matrices M,C,K, independent vs. dependent coordinates formulations, vibration modes for multibody systems with damping, linearization of rotating systems, examples in Maple and applications in Adams.
Multibody systems with flexible bodies: different formulations, component modes synthesis, fixed interface modes, free interface modes, normal modes, constraint modes, CraigBampton method, examples in Maple and applications in Adams.
Contacts in multibody systems: different formulations (continuous vs. instantaneous), modelling of normal forces, modelling of tangential forces, applications in Adams.
Tyre modelling in multibody systems: forces, torques, slip, magic formula, applications in Adams. 

