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Solving constrained mechanical systems by the family of Newmark and α‐methods
Author(s) -
Lunk Ch.,
Simeon B.
Publication year - 2006
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200610285
Subject(s) - newmark beta method , lagrange multiplier , acceleration , property (philosophy) , position (finance) , convergence (economics) , dissipation , mechanical system , equations of motion , mathematics , mathematical optimization , computer science , control theory (sociology) , structural engineering , engineering , finite element method , physics , classical mechanics , artificial intelligence , economics , thermodynamics , economic growth , philosophy , control (management) , epistemology , finance
The family of Newmark and generalized α‐methods is extended to constrained mechanical systems by using simultaneous position and velocity stabilization as key ideas. In this way, the acceleration constraints need not be evaluated, and the overall algorithm is about as expensive as the application of a BDF method to the GGL‐stabilized equations of motion. Moreover, the RATTLE method of molecular dynamics is included as special case. A convergence analysis of the presented α‐RATTLE algorithm shows global second order in both position and velocity variables while the Lagrange multipliers are computed to first order accuracy. Additonally, the property of adjustable numerical dissipation carries over from the unconstrained case.