Now numerically integrate the non-dimensional differential equations. At each step in the integration process, include the Euler parameter constraint K, that is, evaluate the constant K = [ + + } + 2] 2. Integrate given y(0) = ; plot y as a of v (number of revs). Integrate for 4 revs and complete the following simulations: (i) Confirm that if y(0) = 0, all the Euler parameters and y(t) are constant. How do the differential equations tell you that? (ii) Integrate given y(0) = 6 ; for k = -1, 15. Plot the result AK = K-K(0) as a function of v. What is the accuracy of the integration? Is it approximately the same for both values of k? Integrate again for y(0) = 3. For each value of k, plot all three initial value curves on the same plot, i.e., y(0) = 0,3,6. Estimate the period (number of orbits) for one cycle of the angle y. Does the general behavior change for different values of 7(0)?