Multibody Modelling for Vehicle Systems

CONTENT

1. Development Process of Simulation Model
   Ideal objects of engineering sciences. Conceptual model, physical model, simulation model
2. Matrix Formulation of Kinematics
   Matrix of directional cosines, transformation, velocity and acceleration matrices. Basic motions, basic transformation matrices. Method of basic matrices
3. Different Coordinates for Description of Multibody Systems
   Independent and dependent, relative, Cartesian and physical coordinates. Euler angles, Cardan angles, Euler parameters. Kinematical description of open kinematic chain
4. Solution of Kinematical Loops
   Kinematical solution of kinematical loops by method of closed loop, method of disconnected loop, method of removed body, method of natural coordinates, method of compartments (physical coordinates)
5. Numerical Methods for Solution of Multibody Kinematics
   Position, velocity and acceleration problems. Solution of over- and under-constrained system of linear and nonlinear algebraic equations. Special and singular cases of multibody systems
6. Kinematical Synthesis of Multibody Systems
   Engineering design process, formulation of kinematical synthesis, solving procedures, optimization. Synthesis of vehicle suspensions
7. Dynamics of Multibody Systems by Lagrange Equations of Mixed Type
   Lagrange equations of mixed type, assembly of particular expressions. Multibody dynamic formalism by physical coordinates. Interpretation of Lagrange multipliers. Force elements for vehicle modelling
8. Numerical Methods of DAE Solution
   Numerical problems of solution of differential-algebraic equations (DAE). Solution in indepenedent and dependent coordinates, Baumgarte stabilization, coordinate partitioning, projection into independent coordinates
9. Advanced formulation of equations of motion of multibody systems
   Equivalence of Newton-Euler and Lagrange equations. Equations of motion of small vibrations. Dynamics of flexible multibody systems.
10. Practice of multibody modelling
    Multibody modelling for different multibody dynamic formalisms. Example of modelling in Simpack. Modelling of vehicle suspension, modelling of vehicle dynamics

Study materials

1. Lecturing material and hand-outs
2. Stejskal, V., Valasek, M.: Kinematics and Dynamics of Machinery, Marcel Dekker, New York 1996 (basis textbook)