1. LAGRANGE EQUATION x i : Generalized coordinate Q i : Generalized force i=1,2,....,n In a mechanical system, Lagrange parameter L is called as the difference between the kinetic energy and potential energy. Lagrange equation can be written as follows. Here, x i is the generalized coordinate for i th, Q i is the generalized forced for i th. n is the number of degree of freedom of the system, i taking value from 1 to n The reference book given below for this equation can be examined J.H. Williams, Jr., Fundamentals of Applied Dynamics, John Wiley and Sons,Inc., 1996

2. 3 B 2 A 1 O 2k 3c 2k 3c 4 k c k c D f T Inputs: f, T, x 4 xBxB x4x4 Example 1.1 (Continue) Let’s illustrate continuing the Example 1. The equations of kinetic energy, potential energy and generalized forces obtained from virtual work, which are found in previous section, are given again. First, Let’s apply the Lagrange equation to the generalized coordinate of theta.

4. Equation of motion with multi-degree of freedom system Set of linear differential equations