Error Analysis of the Analytical Method

When Orban and Ryckaerf first applied the analytical method, they found that although the constraints were satisfied exactly at some initial time. 

It is possible to reduce the size of the time step such that the system configuration better approximates the constrained system configuration. However, this defies the practical reason for introducing constraints in the first place, namely, the ability to use a larger time step for increased computational efficiency. If the integration algorithm has an error in the coordinates on the order of the time step then in the worst case of holonomic constraints lin- 

The constraints are therefore satisfied only to 0(8z ), and the size of the error in Eq. [13] grows with every time step. Equation [13] should be compared to Eq. [1]. Clearly, for the analytical method to be of practical use, it must be coupled with a correction algorithm to keep the constraints satisfied within a desired tolerance. We describe an approach proposed by Edberg, Evans, and Mor-riss (EEM) and show that it is the simplest special case of the analytical method, with an added constraint correction scheme. 

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