Angle Constraint Versus Triangulation

Point 1 clearly holds for both the matrix method and SHAKE. Because the matrix method is also an iterative approach (albeit a coupled one), the essence of the remarks of point 2 also holds for the matrix method. As stated in point 1, constraining an angle bend with an angle constraint is still applicable when total rigidity is unacceptable, and triangulation is then not a feasible 

Differentiating both sides of Eq. [115] with respect to ), and recalling that both A and C are held constant, we have 

Comparison of Eq. [117] with the angle-constraint convergence condition leads to the following relation between the triangulation bond-stretch tolerance and the corresponding angle tolerance  

Equation [118] translates the tolerance imposed on the triangulation bond stretch into the equivalent tolerance on the corresponding angle and hence can be used for an accurate comparison of the triangulation and angle-constraint approaches. 

The tolerances for bond-stretch and angle-bend constraints are usually expressed as multiples of the constraint bond-stretch and bond-angle values, respectively (st) = (sf) X B, and (at) = (af) X j , where (sf) is the stretch factor or relative bond-stretch tolerance and (af) is the angle-bend factor or relative angle-bend tolerance. Substitution of the tolerance expressions into Eq. [118] yields an analogous relation between the tolerance factors  

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