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Using matlab to find critical points?

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Nick Haufler
Nick Haufler 2016-3-8
评论： Walter Roberson 2016-3-9
For Problem 1 in the attached document, I am struggling to get the right answers. I cant seem to get the correct code to find the critical points and angles.
This is what I have so far:
pos_trap = zeros(size(vel_meas));
pos_trap(1) = 0.35; % Initial position of the piston
for k = 2:length(vel_meas)
pos_trap(k) = pos_trap(k-1) + 0.5*(vel_meas(k-1)+vel_meas(k))*DeltaT;
end
% Check accuracy of Trapezoid estimate
pos_actual = r*cos(w*t)+sqrt(L^2-r^2*sin(w*t).^2);
Error_trap = abs(pos_actual - pos_trap);
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Geoff Hayes
Geoff Hayes 2016-3-9
Nick - I don't have the Symbolic Toolbox so can't comment on whether the above will give the correct answer or not. But it looks like you are using diff correctly to get the first and then second derivative of your function. Do you get similar results if you were to work through the problem by hand?
Walter Roberson
Walter Roberson 2016-3-9
Better would be
syms Th
vel_meas = -0.03*15.708*sin(Th) - 0.03^2*15.708*sin(2*Th)/(2*0.5);
der1 = diff(vel_meas, Th)
CriticalPoints = solve(der1==0, Th)
Note: if you are using a MATLAB version before about R2011b, then change the "derl==0" to just "der1"

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