Newton--Euler equations in general coordinates

Bertold Bongardt, Frank Kirchner

In: Mathematics of Robotics (IMA). IMA Conference on Mathematics of Robotics (IMA-2015) September 9-11 Oxford United Kingdom IMA 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.

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