Time-dependent singular differential equations

Details Time-dependent singular differential equations Time-dependent singular differential equations

2004-10-25

arxiv.org/abs/math-ph/0410051v1

Physics

Mathematical Physics

20 pages

Scientific paper

A geometric framework for describing and solving time-dependent implicit differential equations F(t,x,x')=0 is studied, paying special attention to the linearly singular case, where F is affine in the velocities: A(t,x)x' = b(t,x). This framework is based on the jet bundle of a time-dependent configuration space, and is an extension of the geometric framework of the autonomous case. When A is a singular matrix, the solutions can be obtained by means of constraint algorithms, either directly or through an equivalent autonomous system that can be constructed using the vector hull functor of affine spaces. As applications, we consider the jet bundle description of time-dependent lagrangian systems and the Skinner-Rusk formulation of time-dependent mechanics.

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