Adaptation of the Discretization

One-step methods can be restarted at point b. In this case, changing to a lower order method is not necessary as no past values are used. This is different for 

This involves the knowledge of the order of the discontinuity. Numerical approaches to determine this order work only reliable for orders 0 and 1 [G084]. We therefore suggest to restart the integration method for safety reasons. When restarting a multistep method, much time is spent for regaining the appropriate integration step size and order. The best one can do is to use the information available from the last time interval before the discontinuity in the case of the BDF method for 

To accelerate the restart for multistep methods Runge-Kutta methods can be used to generate the necessary starting values, [SB95]. 

Now we have discussed all steps of the switching algorithm. The overall algorithm is summarized in Fig. 6.3. 

The woodpecker has two degrees of freedom one rotational with respect to the rod (angle 9) and one translational down the rod (height z of point 5). 

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