What is it about?
A general method for studying the vector field of arbitrary higher-order accelerations is described. It is proved that all information regarding the properties of the distribution of high order accelerations is contained in the specified multidual (MD) matrix [5] or the hyper-multidual (HMD) tensor.
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Why is it important?
The development of high-precision robotic systems, artificial vision systems, and molecular dynamics, new space docking procedures, require procedures to calculate higher-order accelerations. The key to the proposed approach starts with the property of rigid body displacements group of forming a Lie group, accompanied by its Lie algebra. A previous result offers an isomorphic representation of the Lie group SE (3) with the group of the orthogonal dual tensors and Lie algebra se (3) ofthe Lie algebra of dual vectors . The results obtained using dual algebras completely solve the problem of finding the field of higher-order accelerations, using a set of results obtained by the previous papers . (6) (PDF) ANALYSIS OF HIGHER -ORDER KINEMATICS ON MULTIBODY SYSTEMS WITH NILPOTENT ALGEBRA THE 32 ND INTERNATIONAL CONFERENCE ON ROBOTICS IN ALPE-ADRIA-DANUBE REGION RAAD 2023. Available from: https://www.researchgate.net/publication/371578575_ANALYSIS_OF_HIGHER_-ORDER_KINEMATICS_ON_MULTIBODY_SYSTEMS_WITH_NILPOTENT_ALGEBRA_THE_32_ND_INTERNATIONAL_CONFERENCE_ON_ROBOTICS_IN_ALPE-ADRIA-DANUBE_REGION_RAAD_2023 [accessed Jun 27 2023].
Perspectives
The results interest the theoretical kinematics, higher-order kinematics analysis in the case of serial manipulator, control theory and multibody kinematics.
Prof. Daniel Condurache
Gheorghe Asachi Technical University of Iasi
Read the Original
This page is a summary of: Analysis of Higher- Order Kinematics on Multibody Systems with Nilpotent Algebra, January 2023, Springer Science + Business Media,
DOI: 10.1007/978-3-031-32606-6_35.
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