A modified HHT method for the numerical simulation of rigid body rotations with Euler parameters

Karim Sherif, Karin Nachbagauer, Wolfgang Steiner, Thomas Lauß

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In multibody dynamics, the Euler parameters are often used for the numerical simulation of rigid body rotations because they lead to a relatively simple form of the rotation matrix which avoids the evaluation of trigonometric functions and can thus save computational time. The Newmark method and the closely related Hilber–Hughes–Taylor (HHT) method are widely employed for solving the equations of motion of mechanical systems. They can also be applied to constrained systems described by differential algebraic equations. However, in the classical versions, the use of these integration schemes have a very unfavorable impact on the Euler parameter description of rotational motions. In this paper, we show analytically that the angular velocity for a rotation about a single axis under a constant moment will not increase linearly but grows slower. This effect, which does not appear for Euler angles, can be even observed if the numerical damping Parameter α in the HHT method is set to zero. To circumvent this problem without losing the advantage of Euler parameters, we present a modified HHT method which reduces the damping effect on the angular velocity significantly and eliminates it completely for α=0.
Original languageEnglish
Pages (from-to)181-202
Number of pages22
JournalMultibody System Dynamics
Issue number2
Publication statusPublished - 15 Jun 2019


  • Numerical time integration
  • Numerical damping
  • Euler parameters
  • Multibody dynamics

Fingerprint Dive into the research topics of 'A modified HHT method for the numerical simulation of rigid body rotations with Euler parameters'. Together they form a unique fingerprint.

Cite this