A simple model of a satellite, orbiting the earth, is given by the differential equation *(t) = r(t)a. r(t) + u(t) where r is the satellite's distance to the earth and o is its angular acceleration, see the diagram below. The satellite has a gas jet engine, which can exert a radial force u. (Linearisation] u(t) r(t), Satellite orbiting the earth. [r(t) a. Introduce the state vector x(t) = and write down the nonlinear state space equations for the system. b. Linearise the state space equations around the stationary point (r,r, u) (r,0, 0). Consider r as the output and give the state space representation of the linear system. Express r in 6 and w.