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Preface; Contents; On the History of Differential-Algebraic Equations; 1 Introduction; 2 The Early Days; 2.1 First Encounter; 2.2 Who Coined the Term DAEs?; 2.3 Kirchhoff, Weierstrass, and Kronecker; 2.4 Euler and Lagrange; 3 The Boom Days; 3.1 The Paderborn Workshops; 3.1.1 The Geneva School; 3.1.2 DAEs and Control Theory; 3.1.3 The Berlin School; 3.2 The Oberwolfach Workshop in 1993; 3.2.1 Differential Equations on Manifolds; 3.2.2 Singularly Perturbed Problems and Regularization; 3.2.3 General Fully Implicit DAEs; 3.2.4 The Flying Wheelset; 3.3 The Oberwolfach Workshop in 1996
3.3.1 A Famous Inequality and Why One Should Never Trust Authorities4 Consolidation; 4.1 The NUMDIFF Conference in 1997; 4.2 Examples of PDAEs; 4.3 Pantograph and Catenary; 4.4 The Oberwolfach Workshop in 2006; References; DAE Aspects of Multibody System Dynamics; 1 Introduction; 2 Constrained Mechanical Systems; 2.1 Equations of Motion; 2.2 Existence and Uniqueness; 2.3 Positive Semi-Definite Mass Matrices, Rank-Deficient Constraint Matrices; 3 From Constrained Mechanical Systems to Multibody SystemDynamics; 3.1 Configuration of Rigid Body Systems
3.2 Model Equations in Multibody System Dynamics3.3 Multibody Formalisms and Topological Solvers; 4 Time Integration Methods for Constrained Mechanical Systems; 4.1 Direct Time Discretization of the Constrained Equationsof Motion; 4.1.1 Time Integration of Second Order Systems by Newmark Type Methods; 4.1.2 ODE and DAE Time Integration Methods for First Order Systems; 4.2 Index Reduction and Projection; 4.2.1 Index-2 Formulation; 4.2.2 Index-1 Formulation; 4.2.3 Drift-Off Effect; 4.2.4 Projection Techniques and Baumgarte Stabilization; 4.2.5 Stabilized Index-2 Formulation; 5 Summary
5 Structured DAE Systems5.1 Semi-Explicit Systems of Index 1; 5.2 Magneto-Quasistatic Systems of Index 1; 5.3 Circuit Equations of Index 1 and 2; 5.4 Stokes-Like Systems of Index 2; 5.5 Mechanical Systems of Index 1 and 3; 6 Other Model Reduction Topics; 6.1 Model Reduction of Periodic Discrete-Time Descriptor Systems; 6.2 Index-Aware Model Reduction for DAEs; 6.3 Parametric Model Reduction; 7 Conclusions; References; Observability of Linear Differential-Algebraic Systems: A Survey; 1 Introduction; 2 Weak and Distributional Solutions; 3 Observability Concepts
3.3.1 A Famous Inequality and Why One Should Never Trust Authorities4 Consolidation; 4.1 The NUMDIFF Conference in 1997; 4.2 Examples of PDAEs; 4.3 Pantograph and Catenary; 4.4 The Oberwolfach Workshop in 2006; References; DAE Aspects of Multibody System Dynamics; 1 Introduction; 2 Constrained Mechanical Systems; 2.1 Equations of Motion; 2.2 Existence and Uniqueness; 2.3 Positive Semi-Definite Mass Matrices, Rank-Deficient Constraint Matrices; 3 From Constrained Mechanical Systems to Multibody SystemDynamics; 3.1 Configuration of Rigid Body Systems
3.2 Model Equations in Multibody System Dynamics3.3 Multibody Formalisms and Topological Solvers; 4 Time Integration Methods for Constrained Mechanical Systems; 4.1 Direct Time Discretization of the Constrained Equationsof Motion; 4.1.1 Time Integration of Second Order Systems by Newmark Type Methods; 4.1.2 ODE and DAE Time Integration Methods for First Order Systems; 4.2 Index Reduction and Projection; 4.2.1 Index-2 Formulation; 4.2.2 Index-1 Formulation; 4.2.3 Drift-Off Effect; 4.2.4 Projection Techniques and Baumgarte Stabilization; 4.2.5 Stabilized Index-2 Formulation; 5 Summary
5 Structured DAE Systems5.1 Semi-Explicit Systems of Index 1; 5.2 Magneto-Quasistatic Systems of Index 1; 5.3 Circuit Equations of Index 1 and 2; 5.4 Stokes-Like Systems of Index 2; 5.5 Mechanical Systems of Index 1 and 3; 6 Other Model Reduction Topics; 6.1 Model Reduction of Periodic Discrete-Time Descriptor Systems; 6.2 Index-Aware Model Reduction for DAEs; 6.3 Parametric Model Reduction; 7 Conclusions; References; Observability of Linear Differential-Algebraic Systems: A Survey; 1 Introduction; 2 Weak and Distributional Solutions; 3 Observability Concepts