The complementary property of Lindelof's work and Chaplygin's work

Lindelof's equation is derived by using the Vakonomic model,which shows tha t Lindelof's work coincides with Vakonomic model. Chaplygin' s equation is derived hy using Chetaev's model, which shows that Chaplygin' s work coinci des with Chetaev's model. On basis of these, by improving the expressions o f Chaplygin's equation and Lindelof's equation, the reasonable transition f rom Chaplygin' s equation to Lindelof's equation is realized, the reasonabl e transition from Lindelof's equation to Chaplygin's equation is realized t oo. Finally, a typical example is given. The work of this paper shows chat, just as the Vakonomic model and Chetaev's model are complementary to each other, Lindelof's work and Chaplygin's work are complementary to each other too.