A similar situation happens with two rotating inertias, each of which is individually modeled using the angle of rotation and the angular velocity. Two states will disappear when the inertias are joined by a rigid shaft. This difficulty can be avoided by replacing differential equations by differential algebraic equations, which have the form F(z, ˙z) = 0, where z ∈ R n . A simple special case is ˙x = f (x, y), g(x, y) = 0, (2.4) where z = (x, y) and F = ( ˙x − f (x, y), g(x, y)). The key property is that the derivative ˙z is not given explicitl