3. Matlab Solvers: A Case Study in Mechanics Suppose we have two objects orbitin

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3. Matlab Solvers: A Case Study in Mechanics Suppose we have two objects orbiting in space, with masses 1- and , rotating around each other. For example, think of the earth and the moon, where the moon moves around the earth at distance 1. (Of course, here both the masses and the distance are normalized.) A third object, which is relatively much smaller and does not affect the motion of the first two, is also orbiting in space. Think of this as a space-ship, or a meteorite. To simplify the analysis, we assume that all trajectories lie in the same plane. We choose the barycenter of mass as the origin of our coordinate system. Moreover, we adopt a rotating frame of coordinates. In this moving frame, the earth and the moon are always located at the points of,y ) = (-, 0), and their barycenter is at (0, 0). We denote by (yi (t), y2(t)) the position of the space ship at time t, w.r.t. this rotating frame of coordinates The equations of motion are: y2 y2 22 1/2 = 0.012277471, JL Notice that, in each of above ODEs, the first two terms account for the Coriolis force, due to the fact that the rotating frame is not an inertial frame. The last two terms account for the gravitational pull of the earth and the moon, respectively. The numbers dE, dM measure the distance of the space ship from the earth and from the moon, respectively. Consider the initial conditions 31 (0) 0.994. yi (0) = 0, U2(0) = 0, 2(0)- -2.0015851063790825 For this particular initial data the solution turns out to be periodic. Indeed, at time t 17.065211656 the rotating object goes back to its initial configuration, and the entire motion is repeated over again You need to do the following:

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the snwer is in image as below

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ODE first order is simple to solve

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