HIGHER-ORDER ACCELERATIONS ON RIGID BODIES MOTIONS. A TENSORS AND DUAL LIE ALGEBRA APPROACH
Abstract: This paper extends the results from velocities and accelerations fields of rigid bodies motion to higher-order accelerations. Using the tensor calculus and the dual numbers algebra, a computing method for studying the higher order acceleration field properties is proposed in the case of the general motion. The vector and tensor invariants in the distribution of the n-th order acceleration field are highlighted. For the case of the spatial kinematics chains, an equation that allows the determination of the n-th order field accelerations are given, using a Brockett-like formulas specific to the dual algebra. The results are free of coordinate and in a closed form. In particular cases the properties for velocities, accelerations, jerks, and hyper-jerks fields are given. This approach uses the isomorphism between the Lie group of the rigid displacements
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