% THE PROJECT
%
clear
%
N=100 %number of points
h=0.1 % step size
ts=20 %starting time
%^
for i=1:N
t1(i)=exp(-2*ts)*sin(pi*ts);
F(i)=-exp(-2*t1(i))*(2*sin(pi*t1(i))-pi*cos(pi*t1(i))); %position
Fv(i)=-exp(-2*t1(i))*((pi^(2)-4)*sin(pi*t1(i))+4*pi*cos(pi*t1(i))); %velocity
Fa(i)=-exp(-2*t1(i))*((6*pi^(2)-8)*sin(pi*t1(i))+(12*pi-pi^(3)*cos(pi*t1(i)))); %acceleration
end
%
for i=1:N
if(i<=2) %forward
Fd(i)=(-F(i+2)+4*F(i+1)-3*F(i))/(2*h);
Fdd(i)=(-F(i+3)+4*F(i+2)-5*F(i+1)+2*F(i))/(h^2);
elseif ((i==N) | (i==N-1)) %backwards
Fd(i)=(3*F(i)-4*F(i-1)+F(i-2))/(2*h);
Fdd(i)=(2*F(i)-5*F(i-1)+4*F(i-2)-F(i-3))/(h^2);
else %center
Fd(i)=(-F(i+2)+8*F(i+1)-8*F(i-1)+F(i-2))/(12*h);
Fdd(i)=(-F(i+2)+16*F(i+1)-30*F(i)+16*F(i-1)-F(i-2))/(12*h^2)
end
end
%
%
figure (1)
plot(t1,F)
title('Rocket position')
xlabel('time(s)')
ylabel('position(m)')
%
figure(2)
plot(t1,Fv,t1,Fd)
title('Rocket velocity')
xlabel('time(s)')
ylabel('velocity(m/2)')
%
figure(3)
plot(t1,Fa,t1,Fdd)
title('Rocket acceleration')
xlabel('time(s)')
ylabel('acceleration(m/s^2)')
%
figure(4)
plot(t1,(Fv-Fd),t1,(Fa-Fdd))
legend('Vel error','Acc Err')
%
figure(5)
subplot(2,2,1),plot(t1,F)
title('Rocket position')
xlabel('time(s)')
ylabel('position(m)')
%
subplot(2,2,2),plot(t1,Fv,t1,Fd)
title('Rocket velocity')
xlabel('time(s)')
ylabel('velocity(m/2)')
%
subplot(2,2,3),plot(t1,Fa,t1,Fdd)
title('Rocket acceleration')
xlabel('time(s)')
ylabel('acceleration(m/s^2)')
%
subplot(2,2,4),
plot(t1,(Fv-Fd),t1,(Fa-Fdd))
legend('Vel error','Acc Err')
