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Many methods have been proposed for the stabilization of higher index differential-algebraic equations (DAEs). Such methods often involve constraint differentiation and problem stabilization, thus obtaining a stabilized index reduction. A popular method is Baumgarte stabilization, but the choice of parameters to make it robust is unclear in practice. Here we explain why the Baumgarte method may run into trouble. We then show how to improve it. We further develop a unifying theory for stabilization methods which includes many of the various techniques proposed in the literature. Our approach is to (i) consider stabilization of ODEs with invariants, (ii) discretize the stabilizing term in a simple way, generally different from the ODE discretization, and (iii) use orthogonal projections whenever possible. The best methods thus obtained are related to methods of coordinate projection. We discuss them and make concrete algorithmic suggestions.
A Hamiltonian system in potential form (formula in the original abstract) subject to smooth constraints on q can be viewed as a Hamiltonian system on a manifold, but numerical computations must be performed in Rn. In this paper methods which reduce "Hamiltonian differential algebraic equations" to ODEs in Euclidean space are examined. The authors study the construction of canonical parameterizations or local charts as well as methods based on the construction of ODE systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an invariant manifold. In each case, a Hamiltonian system of ordinary differential equations is produced. The stability of the constraint invariants and the behavior of the original Hamiltonian along solutions are investigated both numerically and analytically.
Many methods have been proposed for the simulation of constrained mechanical systems. The most obvious of these have mild instabilities and drift problems. Consequently, stabilization techniques have been proposed A popular stabilization method is Baumgarte's technique, but the choice of parameters to make it robust has been unclear in practice. Some of the simulation methods that have been proposed and used in computations are reviewed here, from a stability point of view. This involves concepts of differential-algebraic equation (DAE) and ordinary differential equation (ODE) invariants. An explanation of the difficulties that may be encountered using Baumgarte's method is given, and a discussion of why a further quest for better parameter values for this method will always remain frustrating is presented. It is then shown how Baumgarte's method can be improved. An efficient stabilization technique is proposed, which may employ explicit ODE solvers in case of nonstiff or highly oscillatory problems and which relates to coordinate projection methods. Examples of a two-link planar robotic arm and a squeezing mechanism illustrate the effectiveness of this new stabilization method.
The prepaparation of amorphous, homogeneous blends of zwitterionic polymers and transition metal salts was investigated. Homogeneous miscibility was achieved in many cases up to equimolar amounts of salt, depending on the anion and cation chosen. Various analytical techniques point to a solid state solution of the inorganic ions in the polymer matrix.
The dramatic changes in international relations characterized by the terms "Complex Interdependence" and "Segmentary Globalization" call for new explanation. The author considers the post-modern approaches, a critical analysis of which he presents, to be one possibility to do that. In studies of international policy, these post-modern influences are gaining ground in disputes with realistic and neo-realistic approaches, and they can also clearly be felt in Latin America. Tomassini, based on the historic experiences of Latin America, forcefully calls for an active and constructive incorporation of the region into international developments. For that, Latin-American societies have to establish modern, and open political as well as economic systems which are able to meet those challenges.
Taking the visit of Erich Honecker to China as an example, the author analyses the bilateral GDR-Chinese relations in the 1980s. Based on extensive original research, the objectives as well as disappointed hopes are presented. The author reveals that not Honecker played the "Chinese Card", but he himself became part of Chinese politics. At the same time, the contradictory reaction to that visit in Moscow are documented when, with the election of Gorbachev, first signs of a change in Soviet policy toward China were indicated. Jahresabo: 40,00 € (ermäßigt: 25,00 €)