Consider the second order system x x(x+x) x = x x2(x + x). x2 x =...

 

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Consider the second order system x x(x+x) x = x x2(x + x). x2 x = x2-x = a) Write differential equations for the variables r and in polar coordinates (x x2 = rsin) in a way that their derivatives may depend on r and 0, but not on x1, x2. b) Draw phase portraits (in x1, x2 coordinates) for the cases <0, = 0, and > 0. rcos 0, Consider the second order system x x(x+x) x = x x2(x + x). x2 x = x2-x = a) Write differential equations for the variables r and in polar coordinates (x x2 = rsin) in a way that their derivatives may depend on r and 0, but not on x1, x2. b) Draw phase portraits (in x1, x2 coordinates) for the cases <0, = 0, and > 0. rcos 0,