Abstract
In this paper, using the tensor calculus and the dual numbers algebra, a new computing method for studying the higher-order accelerations field properties is proposed in the case of the general rigid body motion. For the spatial kinematic chains, equations that allow the determination of the \( {\text{n}}^{\text{th}} \) order accelerations field are given, using a Brockett-like formula specific to the dual algebra. The results are coordinate-free and in a closed form. In particular cases, the properties for velocities, accelerations, jerks and jounces fields are given. This approach uses the isomorphism between the Lie group of the rigid displacements \( S{\mathbb{E}}_{3} \) and the Lie group of the orthogonal dual tensors.
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Condurache, D. (2019). Higher-Order Relative Kinematics of Rigid Body Motions: A Dual Lie Algebra Approach. In: Lenarcic, J., Parenti-Castelli, V. (eds) Advances in Robot Kinematics 2018. ARK 2018. Springer Proceedings in Advanced Robotics, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-93188-3_10
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DOI: https://doi.org/10.1007/978-3-319-93188-3_10
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