Theory and formulations

• Theory and formulations
• Introduction to multibody systems
  • Historical development
  • Simulation tools in computational engineering
  • Components of a multibody system
  • Kinematics basics
  • Euler’s and Chasles’s Theorems
  • Degree of freedom – DOF
  • Non-holonomic constraints
  • Dependent and independent coordinates
  • Chebychev-Grübler-Kutzbach criterion
  • Generalized coordinates
  • Reference and current coordinates
• Dynamics: Mechanical principles
  • Newton’s basic principles
  • The Lagrange-d’Alembert principle
  • Generalized Principle of Virtual Work
  • Virtual displacements
  • Generalized Forces
  • Lagrange’s Equations of Motion
  • Multibody formulations: redundant and minimal coordinates
• Frames, rotations and coordinate systems
  • Reference points and reference frames
  • Coordinate systems of frames
  • Homogeneous transformations
  • Rotations
  • Rotation tensor: axis-angle representation
  • Euler angles: Tait-Bryan angles
  • Euler parameters and unit quaternions
• Integration Points
• Model order reduction and component mode synthesis
  • Import of flexible bodies
  • Eigenmodes
  • Hurty-Craig-Bampton modes
  • Computation of stresses and strains for CMS modes
  • Interfaces and boundaries
  • Node weighting
  • Reference conditions