Dynamically equivalent implicit algorithms for the integration of rigid body rotations

Two midpoint‐trapezoid pairs of dynamically equivalent (conjugate) algorithms are derived as compositions of first‐order forward Euler and backward Euler integrators as applied to an incremental form of the initial‐value problem of three‐dimensional rigid body rotation. The algorithms are related to...

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Vydáno v:	Communications in numerical methods in engineering Ročník 24; číslo 2; s. 141 - 156
Hlavní autor:	Krysl, P.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Chichester, UK John Wiley & Sons, Ltd 01.02.2008 Wiley
Témata:	angular momentum conservation composition of maps Computational techniques dynamic equivalence Exact sciences and technology Fundamental areas of phenomenology (including applications) Mathematical methods in physics midpoint rule Munthe-Kaas Runge-Kutta methods Physics rigid body dynamics Solid dynamics (ballistics, collision, multibody system, stabilization...) Solid mechanics symplectic time integration trapezoidal rule Rigid bodies Munthe- Kaas Runge-Kutta methods Numerical integration Initial value problem Three body system Solid dynamic angular momentum conservation midpoint rule Runge Kutta method Long term Modeling Conservation law Time domain method symplectic trapezoidal rule Angular momentum Trapezoidal method Integrator dynamic equivalence Time integration rigid body dynamics composition of maps
ISSN:	1069-8299, 1099-0887
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Popis
Shrnutí:	Two midpoint‐trapezoid pairs of dynamically equivalent (conjugate) algorithms are derived as compositions of first‐order forward Euler and backward Euler integrators as applied to an incremental form of the initial‐value problem of three‐dimensional rigid body rotation. The algorithms are related to the recently developed methodology of the so‐called Munthe‐Kaas Runge–Kutta methods. Selected examples are used to illustrate the excellent long‐term integration properties. Copyright © 2006 John Wiley & Sons, Ltd.
Bibliografie:	ArticleID:CNM963 istex:6DF4A961D584B601E83358D7DFE44FAD947297E0 ark:/67375/WNG-W9PSX0MQ-9 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	1069-8299 1099-0887
DOI:	10.1002/cnm.963