RATTLE for General Holonomic Constraints

The solution for the 7 and It)] using SHAKE was termed RATTLE by Andersen. The material here is new in the sense that the original formulation of RATTLE was for bond-stretch constraints only. The treatment is general- 

The first stage of RATTLE is analogous to SHAKE. The new positions of the particles -I- 8f)) obtained in the current iteration are 

As with SHAKE, iterations over the constraints continue until all are satisfied, within a certain tolerance. When all constraints have been satisfied and the coordinates at (tQ + bt) are available, the forces + 80) can be computed for use in the second stage of RATTLE. In this second stage, the new velocities of the particles [r ( Q + 8f)) obtained in the current iteration are 

iteration over all constraints continues until the constraints on the velocities have been satisfied within a selected tolerance. The entire procedure is then repeated at the next time step. 

As with SHAKE, RATTLE is illustrated in this chapter for the internal coordinate constraints of bond stretch, angle bend, and torsion. For bond-stretch constraints and the first stage of RATTLE, inserting the constraint a ( rj) of Eq. [95] into Eq. [131] yields 

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