** Next:** Introduction

**Note:** A zipped up postscript version
of this paper is also available.

**State Space Projection onto Linear DAE Manifolds Using
Conservation Principles**

**Pieter J. Mosterman
**^{}

Institute of Robotics and System Dynamics

DLR Oberpfaffenhofen

P.O. Box 1116

D-82230 Wessling

`Pieter.J.Mosterman@dlr.de`

### Abstract:

Continuous physical system behavior can be effectively modeled by
differential equations, possibly supplemented by a number of algebraic
constraints. The time-derivative variables form the system state,
and behavior evolves in state space. Algebraic equations define
a manifold in state space to which behavior evolution is
confined. Efficient algorithms exist to solve the additional
constraints on the state variables to give the gradient of behavior along the
manifold. However, initial state values may be such that
they are not on the manifold, and, therefore, a projection is
required before behavior evolution can proceed.
The projection may cause discontinuities in state variables values, and,
therefore, require impulses on their derivatives. This paper applies
physical conservation laws to derive a consistent projection
of state variable values onto the manifold of semi-explicit
DAE systems with linear constraints.
These correspond to a large class of dynamic
system models based on physical principles.

** Next:** Introduction
*Pieter J. Mosterman ER*

*7/27/1998*