3rd derivative of position

Hi.

I have question and I will appreciate If you could help me.

I want to calculate the third derivative of position for discrete numbers.

I used the below code for 2nd derivative and I want to know how is the 3rd?

dx = diff(x);dt=diff(t);
v_x = dx./dt;

dt2 = (dt(1:end-1)+dt(2:end))/2;
a_x = diff(v_x)./dt2;

v_x is velocity and a_x is acceleration

thanks

Answer 1

[Azzi Abdelmalek]

dt=t(2)-t(1)
dy=gradient(y,dt)
dy2=gradient(dy,dt)
dy3=gradient(dy2,dt)
t=t(1:end-3)
dy3=dy3(1:end-3)
plot(t,dy3)

%or using diff

t=0:0.1:2
y=t.^4
y3=diff(y,3)
dt=diff(t)
dy3=y3./dt(1:end-2)

[Erin Browne]

what would t be equal to?

[Torsten]

t can be any vector of the same length as y with t(i+1) - t(i) = dt = constant for all i.

Answer 2

[SHAHZAD]

v_x = dx./dt;

dt2 = (dt(1:end-1)+dt(2:end))/2;

a_x = diff(v_x)./dt2;