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A new Leapfrog scheme for rotational motion in 3D
Author(s) -
Mariotti C.
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5165
Subject(s) - rotation (mathematics) , scheme (mathematics) , torque , rigid body , rotation around a fixed axis , computer science , code (set theory) , element (criminal law) , taylor series , interpretation (philosophy) , discrete element method , series (stratigraphy) , motion (physics) , algorithm , mathematics , classical mechanics , physics , artificial intelligence , mathematical analysis , mechanics , paleontology , set (abstract data type) , biology , political science , law , thermodynamics , programming language
Summary Discrete element codes use complex geometric solid particles, so it is necessary to integrate three‐dimensional rigid‐body rotation correctly with external torque. This article presents an interpretation of the Leapfrog scheme. We begin with some rotation formulae before presenting an efficient and high‐order recurrent Taylor series method for rotation. Integrating this method with Leapfrog interpretation provides a complete scheme for rotational motion with external torque. This new Leapfrog scheme has been integrated into the CeaMka3D Discrete Element code, and we present some verifications and simulations to illustrate the capabilities of this scheme. Copyright © 2016 John Wiley & Sons, Ltd.