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OBJECTIVES
Let us consider the second order differential equation x''(t)=g(t,x(t),x'(t)). By introducing the new function y(t)=x'(t) we may rewrite this equation as the coupled pair of first order equations x'(t)=y(t) y'(t)=g(t,x(t),y(t)). More generally one is often interested in considering more general coupled differential equation of the form x'(t)=f(t,x(t),y(t)) y'(t)=g(t,x(t),y(t)), where f and g are given functions. A good way to interpret these equations is as follows: (x(t),y(t)) is the position of a leaf subject to wind whose velocity at the space-time point (x,y,t) has x-component given by f(t,x,y) and y-component given by g(t,x,y). The MATLAB program "pplane5" should help you understand this interpretation in the case where f and g do not depend on t.
x'=sin(y-x/5) y'=y^2*sin(x)/4. Make the plot as interesting as you can. You should hand in your pictures and explanation for this lab. [ Objectives | Background | Exercises ] |
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