MODELING AND SIMULATION OF MECHANICAL SYSTEMS

Kinematics of multibody systems: translation and rotation matrices for three-dimensional 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 three-dimensional systems, problems related to redundant constraints, position and velocity initial analysis, analytical examples 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, 'Gear-Gupta-Leimkuhler' and 'Hiller-Anantharaman' formulations for the reduction of the DAE index, equilibria, analytical examples 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, analytical examples and applications in Adams.

Multibody systems with flexible bodies: different formulations, component modes synthesis, fixed interface modes, free interface modes, normal modes, constraint modes, Craig-Bampton method, analytical examples and applications in Adams.

Contacts in multibody systems: different formulations (continuous vs. instantaneous), modelling of normal forces, modelling of tangential forces, analytical examples and applications in Adams.

Tyre modelling in multibody systems: forces, torques, slip, magic formula, applications in Adams.