THE COMPLEMENTARY PROPERTY OF LINDELF’S WORK AND CHAPLYGIN’S WORK

Lindelf’s equation is derived by using the Vakonomic model,which shows that Lindelf’s work coincides with Vakonomic model. Chaplygin’s equation is derived by using Chetaev’s model, which shows that Chaplygin’s work coincides with Chetaev’s model. On basis of these, by improving the expressions of Chaplygin’s equation and Lindelf’s equation, the reasonable transition from Chaplygin’s equation to Lindelf’s equation is realized, the reasonable transition from Lindelf’s equation to Chaplygin’s equation is realized too. Finally, a typical example is given. The work of this paper shows that, just as the Vakonomic model and Chetaev’s model are complementary to each other, Lindelf’s work and Chaplygin’s work are complementary to each other too.

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

Lindelöf' s equation is derived by using the Vakonomic model, which shows that Lindelöf' s work coincides with Vakonomic model. Chaplygin' s equation is derived by using Chetaev' s model, which shows that Chaplygin' s work coincides with Chetaev' s model. On basis of these, by improving the expressions of Chaplygin' s equation and Lindelöf' s equation, the reasonable transition from Chaplygin' s equation to Lindelöf's equation is realized, the reasonable transition from Lindelöf's equation to Chaplygin' s equation is realized too. Finally, a typical example is given. The work of this paper shows that, just as the Vakonomic model and Chetaev's model are complementary to each other, Lindelöf' s work and Chaplygin' s work are complementary to each other too.