Linear spaces for index 2 differential-algebraic equations (Q1974724)

The author studies the homogeneous index 2 differential-algebraic equation \[ A(t)y'(t)+ B(t)y(t)=0 \] and the adjoint equation \[ A^T(t) \varphi'(t)- (B^T(t)- A^T(t)') \varphi(t)=0. \] The solution spaces of the given equations are described by means of canonical projectors and are represented as solutions to linear systems of equations. A simple method for calculating consistent initial values is provided and relations among the representation of the solution spaces, the constraint manifolds, a suitable index reduction and the computation of consistent initial values are derived.