How to Get Second Derivative in ode45 solver?

Dear MATLAB users;

I would like to solve a nonlinear equation using ode45. ode45 solver provides time (t), position (x), velocity (x_dot) .

I need acceleration , second derivative (x_dotdot). However, I can't get x_dotdot as output from ode45. I looked at the options/parameteres of ode45. I couldn't find there information about that.

I know that I can get x_dotdot, using x_dot numerically by subtraction of xdot(step n) and xdot(n+1 step), by typing extra codes. But I just wondered if it is possible to do it without writing codes? Is it possible to get second derivative (x_dotdot) of ode45 by using options in ode45?

Thanks in advance.

Ercan

Answer 1

[Sam Chak]

Hi @ercan duzgun

You don't need to..., because you can see the elephant in the room (not sure if this is the correct metaphorical idiom; I'm not good at English idioms).

Say the system is given by .

f = @(t, x) [x(2); - 2*x(2) - x(1)];
[t, x] = ode45(f, [0 10], [1 0]);
xddot  = - 2*x(:,2) - x(:,1);       % the acceleration, second derivative (x_dotdot)
plot(t, xddot), grid on, xlabel('t')

[ercan duzgun]

Dear @Sam Chak thank you very much for your response. Really, you are right, it was really the elephant in the room :) . I am surprised how I didn't notice this very obvious thing. Thank you for showing me, explaining me in detailed.

Kind regards,

Ercan