Computer-Aided Simulation of Mechanical Systems

  • Mathematical tools: localization in space, vectors, homogeneous transformation matrices, rotation tensors.
  • Elements of a mechanical system: bodies, joints, force elements.
  • Kinematic analysis: degrees of freedom, configuration parameters, velocities, accelerations, kinematic matrices.
  • Numerical construction of equations of motion (minimal and Cartesian coordinates).
  • Numerical integration: ODE, DAE, accuracy, stability.
  • Other numerical problems: static analysis, assembly, eigen analysis
  • Machine dynamics: modelling of contacts with and without friction.
  • Simulation of vehicles on roads and on rails: tyre/road and wheel/rail contact force elements and practical simulations.
  • Behavioral equations of some usual actuators: DC motor, voice coil, piezoelectric material and hydraulic jack. Coupling between the mechanical system and the actuators.
  • Time-domain model of transfer functions (namely PID control). State feedback control. Equations of the controlled system in continuous or discrete-time.
  • Introduction to robotics.
  • Modeling and simulation of aerial multirotor drones: representation of propellers, linearization about hovering, attitude control, trajectory control.