# Consider the chaotic motion of a DDP for which the Liapunov exponent is λ = 1, with time… 1 answer below »

Consider the chaotic motion of a DDP for which the Liapunov exponent is λ = 1, with time measured in units of the drive period as usual. (This is very roughly the value found in Problem 12.13.) (a) Suppose that you need to predict ∅ (t) with an accuracy of 1/100 rad and that you know the initial value ∅ (0) within 10-6rad. What is the maximum time tmax for which you can predict ∅ (t) within the required accuracy? This tmax is sometimes called the time horizon for prediction within a specified accuracy. (b) Suppose that, with a vast expenditure of money and labor, you manage to improve the accuracy of your initial value to 10-9radians (a thousand-fold improvement). What is the time horizon now (for the same required accuracy of prediction)? By what factor has tmax improved? Your results illustrate the difficulty of making accurate long-term predictions for chaotic motion.

Problem 12.13

You can see in Figure 12.13 that for y = 1.105, the separation of two identical pendulums with

### Save your time - order a paper!

Get your paper written from scratch within the tight deadline. Our service is a reliable solution to all your troubles. Place an order on any task and we will take care of it. You won’t have to worry about the quality and deadlines

Order Paper Now

Figure 12.13