Consider the ellipsoid V(x, y, z) = rx2 + y2 + (z 2r) 2 = c > 0. (a) Calculate dV/dt
Chapter 9, Problem 5(choose chapter or problem)
Consider the ellipsoid V(x, y, z) = rx2 + y2 + (z 2r) 2 = c > 0. (a) Calculate dV/dt along trajectories of the Lorenz equations (1). (b) Determine a sufficient condition on c so that every trajectory crossing V(x, y, z) = c is directed inward. (c) Evaluate the condition found in part (b) for the case = 10, b = 8/3, r = 28.
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