3.24The equation of motion is ()3Fxxxmx=−=±±. For simplicity, let m=1. Then 3xxx=−±±. This is equivalent to the two first order equations … xy=±and 3yxx=−±(a) The equilibrium points are defined by ()()311xxxxx−=−+=0Thus, the points are: (-1,0), (0,0) and (+1,0). We can tell whether or not the points represent stable or unstable points of equilibrium by examining the phase space plots in the neighborhood of the equilibrium points. We’ll do this in part (c). (b) The energy can be found by integrating 3dyyxxdxxy−==±±or or ()3y dyxxdxC=−+∫∫224224yxxC=−+` In other words … 242242yxxETVC=+=+−=. The total energy C is constant. (c) The phase space trajectories are given by solutions to the above equation
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