Angular Velocities, Twirls, Spins and Rotation Tensors in the Continuum Mechanics Revisited

  • Konstantin NaumenkoEmail author
  • Holm Altenbach
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 89)


In the classical continuum mechanics several quantities related to angular velocity of rotation are introduced. Examples include vorticity vector, twirl tensors and logarithmic spin. Furthermore the corresponding rotation tensors can be defined to capture the orientation of triads. All of these quantities are measures of accompanying rotational motion and can be related to the deformation and velocity gradient. Such relationships are crucial for constitutive modeling of material behavior. The aim of this contribution is to recall classical definitions of rotation-like quantities and to present several new relationships between them.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für MechanikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

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