The Rotating Rigid Body Model Based on a Non-twisting Frame
| العنوان: | The Rotating Rigid Body Model Based on a Non-twisting Frame |
|---|---|
| المؤلفون: | Cristian Guillermo Gebhardt, Ignacio Romero |
| المصدر: | Journal of Nonlinear Science 2020 (2020) |
| بيانات النشر: | Springer Science and Business Media LLC, 2020. |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | Rigid body models, FOS: Physical sciences, Physics - Classical Physics, Conservation law, Kinetic energy, 01 natural sciences, Governing equations, Unit vector, Rigid structures, 0103 physical sciences, FOS: Mathematics, Rotating rigid body model, Momentum integration, Orthogonal unit vectors, ddc:530, Mathematics - Numerical Analysis, ddc:510, 0101 mathematics, Bodies of revolution, 010301 acoustics, Mathematical Physics, Conservation laws, Mathematics, Nonholonomic system, Rotating rigid body, Holonomic, Applied Mathematics, Mathematical analysis, Frame (networking), General Engineering, Classical Physics (physics.class-ph), Numerical Analysis (math.NA), Mathematical Physics (math-ph), Rigid body, Dewey Decimal Classification::500 | Naturwissenschaften::510 | Mathematik, Non-twisting frame, 010101 applied mathematics, Kinetics, Modeling and Simulation, Numerical results, Dewey Decimal Classification::500 | Naturwissenschaften::530 | Physik, Conservation properties, Structure preserving integration, Rotation (mathematics) |
| الوصف: | This work proposes and investigates a new model of the rotating rigid body based on the non-twisting frame. Such a frame consists of three mutually orthogonal unit vectors whose rotation rate around one of the three axis remains zero at all times and, thus, is represented by a nonholonomic restriction. Then, the corresponding Lagrange–D’Alembert equations are formulated by employing two descriptions, the first one relying on rotations and a splitting approach, and the second one relying on constrained directors. For vanishing external moments, we prove that the new model possesses conservation laws, i.e., the kinetic energy and two nonholonomic momenta that substantially differ from the holonomic momenta preserved by the standard rigid body model. Additionally, we propose a new specialization of a class of energy–momentum integration schemes that exactly preserves the kinetic energy and the nonholonomic momenta replicating the continuous counterpart. Finally, we present numerical results that show the excellent conservation properties as well as the accuracy for the time-discretized governing equations. |
| تدمد: | 1432-1467 0938-8974 |
| DOI: | 10.1007/s00332-020-09648-3 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::266182e7af432aaa93570cb83806cf7a https://doi.org/10.1007/s00332-020-09648-3 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....266182e7af432aaa93570cb83806cf7a |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 14321467 09388974 |
|---|---|
| DOI: | 10.1007/s00332-020-09648-3 |