Newton--Euler equations in general coordinates
Bertold Bongardt, Frank Kirchner
In Mathematics of Robotics (IMA), (IMA-2015), 09.9.-11.9.2015, Oxford, IMA, St Anne’s College
University of Oxford, 2015.
For the computation of rigid body dynamics, the Newton-Euler equations represent
a crucial relation unifying the laws of motion by Newton and Euler using the language
of instantaneous screws. Typically, Newton-Euler equations are stated in spatial or in
body coordinates, respectively. In this paper, a general formulation of Newton-Euler
equations is provided for arbitrary reference systems. In particular, the general form
unifies the known equations in spatial and body coordinates. To the best of the authors'
knowledge, this relation between the spatial and the body form has not been reported
in literature. The novel formulation is based on the concept of time differentiation with
respect to moving reference systems.