Numerical Reduction to State Space Form

If this equation is then written in first order form, the state space form of the linear mechanical system consisting of 2Uy first order differential equations is obtained 

The same procedure but with premultiplication by G results in an expression for the generalized constraint forces 

2 Numerical Reduction to the State Space Form of Linear Time Invariant Systems 

As V is not uniquely defined, there are several alternative procedures for numerically determining the matrix V. The central criterion for comparing these procedures will be the condition of the matrix 

As the QR decomposition is more reliable, its use will be described here briefly. For details see [FW84]. 

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