alpha = %pi/4;
theta_e = (%pi/2 - alpha):(-0.005):(alpha - %pi/2);
k = 1/sin(alpha);
n = size(theta_e, "*");

deff("y = fx(x)", "y = atan(sin(x)./(k - cos(x)))");
deff("y = fv(x)", "y = (k*cos(x) - 1)./(k^2 - 2*k*cos(x) + 1)");
deff("y = fa(x)", "y = -sin(x)./(k^2 - 2*k*cos(x) + 1).^2");
deff("y = fj(x)", "y = -(cos(x) - 4*k*(sin(x).^2))./(k^2 - 2*k*cos(x) + 1)./...
    (k^2 - 2*k*cos(x) + 1)");

x = fx(theta_e);
maxx = max(x);
x = 1/maxx*x;

v = fv(theta_e);
maxv = max(v);
v = 1/maxv*v;

a = fa(theta_e);
maxa = max(a);
a = 1/maxa*a;

j = fj(theta_e);
maxj = max(abs(j));
j = 1/maxj*j

maxth = max(theta_e);
pos = 1/maxth*theta_e

scf(0);
clf;

subplot(4, 1, 1)
plot(pos, x)
xtitle("Position angulaire", "t", "$\theta_\mathrm{s}$")

subplot(4, 1, 2)
plot(pos, v)
xtitle("Vitesse angulaire", "t", "$\omega_\mathrm{e}$")

subplot(4, 1, 3)
plot(pos, a)
xtitle("Accélération angulaire", "t", "$\alpha_\mathrm{e}$")

subplot(4, 1, 4)
plot(pos, j)
xtitle("À-coup angulaire", "t", "$j_\mathrm{e}$")