Critical study of Newmark scheme on manifold of finite rotations. (English) Zbl 1002.70003
Summary: We show that the usual material form of Newmark-time-stepping scheme of finite rotations is only a simplified version of the correct formula. This is because spin material rotation vectors, angular velocity vectors and angular accelerations vectors belong to different tangential vector spaces of a manifold at separate time moments. Then, we give corrected Newmark-time-stepping schemes for material description and for spatial description.
MSC:
| 70-08 | Computational methods for problems pertaining to mechanics of particles and systems |
| 70E17 | Motion of a rigid body with a fixed point |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
Keywords:
finite rotations; spin material rotation vectors; angular velocity vectors; angular accelerations vectors; tangential vector spaces; corrected Newmark-time-stepping schemes; material description; spatial descriptionReferences:
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