Integrating algorithms for integrable affine constraints

This letter presents integrating algorithms for affine con straints defined on a manifold. We first explain definition and geomet ric representation of affine constraints. Next, we derive integrating algo rithms to calculate independent first integrals of affine constraints for the two cases where the they are completely integrable and partially noninte grable. Moreover, we prove the existence of inverse functions in the algo rithms. Some examples are also shown to verify our results.