Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MV

Notes on the module handbook of the department Mechanical and Process Engineering

Die hier dargestellten veröffentlichten Studiengang-, Modul- und Kursdaten des Fachbereichs Maschinenbau und Verfahrenstechnik ersetzen die Modulbeschreibungen im KIS und wuden mit Ausnahme folgender Studiengänge am 28.10.2020, bzw. am 13.01.2021 verabschiedet.


Course MV-MEC-86678-K-4

Dynamics of Machines (3V+1U, 5.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 5.0 CP 94 h
3 V Lecture 42 h
1 U Lecture hall exercise class 14 h
(3V+1U) 5.0 CP 56 h 94 h


CP, Effort 5.0 CP = 150 h
Position of the semester 1 Sem. in WiSe
Level [4] Bachelor (Specialization)
Language [DE] German
Area of study [MV-MEC] Mechatronics in Mechanical and Automotive Engineering
Additional informations
Livecycle-State [NORM] Active


  • Rigid body kinematics: coordinate transformation; kinematic transformation; virtual displacements.
  • Fundamentals of mechanics: force and virtual work; axioms of mechanics; the principle of linear and angular momentum.
  • Rigid body kinetics: mass, inertia tensor; kinetic energy, linear and angular momentum; equations of motion.
  • Multibody systems: minimum coordinates, degrees of freedom, constraints; projected Newton-Euler equations; Euler-Lagrange equations (1/ 2 kind); equation of motion; linearization; multibody system classes (MK, MGK, MDK, MDGK, MDNGK).
  • Simple examples: pendulum systems; coupling oscillators. Simple oscillators: solution approaches; state-space representation; free and forced oscillations; resonance.
  • Oscillator systems: solution approaches; MK systems (free and forced oscillations); resonance, apparent resonance, amortization. MDK systems (proportional damping, weak damping, tuned mass damper).
  • Stability analysis: concept and definitions; stability criteria.
  • Applications: quadcopter, robot with two degrees of freedom, bicycle, vehicle dynamic models, wind turbine.

Competencies / intended learning achievements

1. Lecture

Students will obtain solid basic knowledge to analyze the dynamic behavior of different classes of mechanical multibody systems and will be able to:

  • systematically model and analyze fundamental mechanical systems with multiple degrees of freedom based on the basic principles of mechanics, in particular, Euler-Lagrange and Newton-Euler equations
  • acquire and apply a systematic approach to the equations of motion of multibody systems
  • linearize nonlinear equations of motion
  • decouple and solve systems of linear differential equations describing the behavior of multiple coupled oscillators using regular state transformations
  • understand special linear oscillators and system classes (MK, MGK, MDK, MDGK, MDNGK) and characterize them with respect to stability and performance in time and frequency domains
  • characterize free and forced oscillations as well as phenomena of resonance, apparent resonance, and amortization for special system classes, in particular for MK and MDK systems in time and frequency domains
  • perform stability analysis for different mechanical systems and to derive stability criteria.

2. Exercises

Based on concrete exercises, the knowledge imparted in the lectures is consolidated based on concrete problems so that the students can:

  • understand the structure of multibody systems and perform the steps required for the mathematical modeling, e.g. determination of an inertial system and body-attached coordinate systems, specification of the relevant kinematic and dynamic quantities, etc.
  • define the quantities required to describe the system behavior (position, velocity, acceleration, angular velocity, angular acceleration vectors as well as inertia tensors, force and moment vectors, etc.) in a different body- and space-attached coordinate systems
  • define rotation matrices for the systematic transformation of quantities between different coordinate systems
  • mathematically model mechanical multibody systems by applying Euler-Lagrange, or Newton-Euler, and projected Newton-Euler equations
  • formulate linear and nonlinear equations of motion and linearize nonlinear differential equation systems
  • systematically decouple, solve and analyze linear coupled differential equation systems applying regular state transformations
  • perform stability analysis for linear systems of different system classes and apply stability criteria
  • dynamically model mechanical systems with multiple degrees of freedom using computer algebra programs (e.g., MAPLE)
  • solve nonlinear differential equation systems using Matlab/Simulink to simulate multibody systems and analyze their behavior
  • model and analyze mechanical systems and structures, e.g., from the fields of mechanics, automotive engineering, vehicle dynamics, robotics, etc., systematically and, if required, with the help of computer-aided design


  • N. Bajcinca: “Maschinendynamik”, Skriptum (WS 2018/19), TU Kaiserslautern.
  • K. Klotter: “Technische Schwingungslehre”, Band 1&2, Springer-Verlag Berlin Heidelberg, 1960.
  • U. Fischer, W. Stephan: “Mechanische Schwingungen”, Hanser Fachbuchverlag , 1993.


Board, print and digital media, reprints available on the Internet. For further information and course materials please consider the corresponding OLAT-course.

Requirements for attendance (informal)

Higher mathematics, engineering mechanics


Requirements for attendance (formal)


References to Course [MV-MEC-86678-K-4]

Module Name Context
[MV-MEC-22-M-4] Dynamics of Machines P: Obligatory 3V+1U, 5.0 LP