function Fig_5()
x=-50:1:50; % 50 samples per second
close all;
f2=figure;
speed=.92*exp(-(x/15).^2);
acc=get_acceleration(x,0,speed)/5;
acc0=get_acceleration0(x,0,acc);
th=smooth_theta2(acc,1-exp(-.1));
ff=90; fg=.8;

subplot(2,3,1)
plot(x,[speed*fg; acc*ff*fg*.8; acc*ff]');

set(gca,'YTick',-1:1,'XTick',-100:50:100);
axis([-50 50 -1 1])
axis square
% hold on;

subplot(2,3,2)
plot(x,[speed*fg; acc*ff*fg*.8; acc0*ff]');
set(gca,'YTick',-1:1,'XTick',-100:50:100);
axis([-50 50 -1 1])
axis square

subplot(2,3,3)
plot(x,[speed*fg; acc*ff*fg*.8; th*ff]');

set(gca,'YTick',-1:1,'XTick',-100:50:100);
axis([-50 50 -1 1])
axis square
[corr(speed',acc') corr(acc',acc');
corr(speed',acc0') corr(acc',acc0');
corr(speed',th') corr(acc',th')]




function acc=get_acceleration(x,x0,speed)
x=x-x0;
acc=[0 speed(3:end)-speed(1:end-2) 0]/2;


function acc=get_acceleration0(x,x0,acc)
acc(acc<0)=0;