How to create a Matlab object that simulates a spring-mass system without Simulink

I am trying to model a dynamic system (e.g., a spring-mass system) withing a big project, that may be deployed on a machine that doesn't have Simulink.

I would like to create a spring-mass system object, which has a method that takes time as input and return the position, and that stores all the history of states, to be used for the numerical integration.

How can I do it, without SImulink?

Note: I am aware of ODE solvers (e.g., ode45), but my problem with these solvers is that they solve for the all time steps at once, which contrary to what I need. I need to solve for only one time step, as needed.

Thanks :)

Answer 1

[Sam Chak]

@Mahmoud Elzouka

If the spring-mass system is non-stiff, and you want to solve for only one step time, then the conventional Runge–Kutta 4th-order formula should be good enough for the job.

For example, given the dynamical system:

and the initial value ,

select a sufficiently small step size h, and compute the following

to obtain 1-step propagated solution:

[Mahmoud Elzouka]

Thanks @Sam Chak for the solution. It is similar to what I am currently doing.

I was hoping Matlab can give us access to the Simulink-like classes, rather than implement the numerical technique of handling the DE.