How to use ode45 in this case?

Hello,

I have the variable ydd (y double dot) that I want to integrate twice to get the variable y.

The formula of ydd is:

ydd = -tan(phi).*(zdd + gravity)

where phi, zdd are vectors of size (1xn) containing different angles and accelerations at each time instant.

And, gravity is also a vector of size (1xn) containing a constant value (which is 9.81) repeated n times.

So, ydd is also a (1xn) vector containing different accelerations at each time instant.

How can I use ode45 to integrate ydd twice?

Thank you for taking the time to read my question.

Answer 1

[Torsten]

ydot = y'(t0) + cumtrapz(t,-tan(phi).*(zdd+gravity));

y = y(t0) + cumtrapz(t,ydot),

plot(t,y)

where t is your (1xn) vector of times (t0,...,t_(n-1)) and y(t0) and y'(t0) are initial conditions (position and velocity at t=t0, respectively).

[Elie Hatem]

Thank you for your response. I just tried it. I am having a problem with scalar spacing.

I just want to point out that the time vector t is between 0 and 1.98 with a step of 0.01.

Can this be done with the cumtrapz function or do the values in the t vector need to be integers?

Moreover, does that mean that ode45 does not work in this case?

[Torsten]

t can be arbitrarily spaced, but must be increasing and of the same length as the other vectors, namely n.

You could use ODE45 for a solution, but since your equation only depends on t and not on y, it would be overkill to use this solver.

If you want to compare results, take a look at the example "ODE with time-dependent terms" in the ODE45 documentation. It can easily be adapted to solve your application.

[Elie Hatem]

Alright I will check and compare both solutions. Thanks for your help!