Here is a system to ODE i am trying to solve:
w(t) = x(t) + x'(t) + w(t-a)
x''(t) = x'(t) + w(t)
How can i solve this kind of ODE with delay in time?
I am currently studying the phase portrait a differential equation:
diff(y(t), t, t) = -piecewise((diff(y(t), t))*y(t) <><>
Initial conditions are:
y(0) = 1; , diff(y(0), t) = 0;
The phase portrait plots diff(y(t),t) with respect to y(t).
I achieved the phase portrait using Simulink; with a few gain blocks, a switch and a X-Y scope, easily enough.
When i was done, i wondered if i could analyze the equation with a more mathematical approach. I decided to try and plot the phase portrait using Maple 11. I have tried various commands to solve the differential equation with Maple 11 but so far i have confused myself.
Here are my questions:
1) How do i perform small-angle approximation (linearization) on a nonlinear DE using Maple. This is necessary to create a state-space representation of the DEs. By small-angle approximation i mean that:
theta(t)^2 = 0
and so on....
I tried using manual substitution using the "subs" command. It is not a very feasible method. I have tried "dsolve" command. Not what i want since i only want to linearize the DEs and not solve for a particular angle.
2) My second question is regarding defining outputs of the "DiffEquation" command. Usually it will go: