Is it possible to do a collision analysis of a mass-spring system in Matlab?

Dear all,

I'm relatively new to Matlab. As below, I want to observe the path of a wheeled system moving to the left with the linear velocity V after encountering the bump. Is it possible to accomplish this via Matlab? If so, how would you recommend me to proceed?

[Sam Chak]

Can you describe the meaning of the path? Better sketch it on the image.

By the way, you can learn MATLAB programming, and derive the mathematical model from the laws of physics at the same time.

Looks like m1 is influenced by the spring element k1. If there is no damping element, then the system is bound to oscillate.

[Raj]

@Sam Chak The instantaneous position of the wheel's center of mass (shown in red).

[Sam Chak]

Hi @Raj

Good! Now you can start deriving the model. Now you can apply the Euler–Lagrange equation to derive the equations of motion for the wheeled system.

By the way, if the wheeled system travels very slowly, m/s, like the rovers on the moons or asteriods, then I think the path almost traces the surface texture, something as shown by the red curve.

Answer 1

[John D'Errico]

Is it possible? Of course.

First, learn MATLAB. Start with the Onramp tutorials.

At that point, the path you take would depend on your choice, and where you wanted to move forwards. You could decide to model this system using a system of ODEs. So then you might formulate the governing differential equations, and solve them using the ODE suite of tools in MATLAB, perhaps ODE45 or ODE23S, etc.

That last step will be a big one, so you would need to learn about how to formulate the equations of such a physical system. That alone might require courses in differential equations, and modeling. (I don't know your level of mathematical sophistication, so how can I know what you need to learn?)

Alternatively, you could decide to learn tool like Simulink, and the Simscape family of products. In that suite, I see this toolbox:

https://www.mathworks.com/products/simscape-multibody.html

which seems appropriate. The nice thing is, those tools do much of the work for you. But personally, I think actually understanding the fundamental basis they are built on is crucial. So I would advocate for a mixed approach, where you learn how to formulate and solve problems using ODE tools, but also learn to use the more sophisticated tools available.