Example 6.8 Double pendulum is shown in the figure. The length of each pendulum is 21,and the mass of each pendulum is m.Each X pendulum is applied with gravitational force.The kinematic driver is given by Length 27 Mass m ,-4- y2 8 1.Write the acceleration constraint equation X 2.Write the Lagrange equation of the first kind 2 3.Write the mixed algebraic-differential equation 4.Find the Lagrange multipliers 5.Give a physical interpretation of each Lagrange Length 21 x2 multiplier Mass mExample 6.8 x1 y1 C1 x y 1 g x2 y2 C2 2 Length 2l Mass m Length 2l Mass m Double pendulum is shown in the figure. The length of each pendulum is 2l, and the mass of each pendulum is m. Each pendulum is applied with gravitational force. The kinematic driver is given by 2. Write the Lagrange equation of the first kind 1. Write the acceleration constraint equation 3. Write the mixed algebraic-differential equation 5. Give a physical interpretation of each Lagrange multiplier 4. Find the Lagrange multipliers 0 15 2 3 15 5 2 1 1                 t t D       