A generalized geometric framework for constrained systems
A geometric framework for constrained dynamical systems of the form \(A(x)x'=F(x)\) is presented. The framework is used to describe a general type of first order differential equations on a manifold. In this paper these systems are called linearly constrained systems. A stabilization algorithm is devised and discussed in order to solve the equation of motion. The formalism includes the presymplectic and Lagrangian formalisms as well as higher order Lagrangians. In numerical analysis the system \(A(x)x'=F(x)\) is called a linearly implicit differential algebraic equation (DAE). The stabilization algorithm of this paper consists of the construction of a sequence of manifolds. This is very similar to the recent constructions of Rabier, Reich, and Rheinboldt developed in the numerical analysis literature of DAEs.
first order differential equations on a manifold
linearly implicit differential algebraic equation
scientific article; zbMATH DE number 118414
scientific article