Free moving particle with mass m (three degrees of freedom); (b) particle with mass m moving in the gravitational field at the surface of the earth: vertical motion of a falling object (one degree of freedom); (c) particle with mass m moving in the gravitational field at the surface of the earth: motion of a projectile (two degrees of freedom). 3. derive euler-lagrange equations (ele) for the three mechanical systems (a, b, and c) in the previous problem 2.