Social Force and Newton Third Laws

[godisreal]

The social force does not agree with Newton 3rd Law in its mathematical expression. However, the model is widely applied in pedestrian motion. Pedestrian motion definitely is within Newton Laws. So any comments or insight about this issue? @chraibi

I suppose the model is consistent with Newton 1st and 2nd Laws. However, the social force does not agree with Newton 3rd Law (actio=reactio). That seems a serious problem. Someone said the particle does not need to follow Newton Laws. However, pedestrian are low speed object in the macroscopic world, and if social force model is used for pedestrian motion, it should be consistent with Newton Laws.

[godisreal]

If the model agrees with Newton laws, many well-known methods can be used to study the model such as conservation of energy and momentum. In contrast if the model is not within Newtonian dynamics, the above methods cannot be applied.

I have created a short manuscript to address this problem, explaining that the model is consistent with Newton Laws. Your idea or contribution are much welcome and appreciated. Please feel free to share your insight by using this issue trackers, or give any input to the manuscript as below.

https://github.com/godisreal/group-social-force/blob/master/doc/SFCrowd2020.tex

[chraibi]

Thanks for mentioning me in this issue.

Pedestrian motion definitely is within Newton Laws

I don't know exactly if this is true, but the model is basically used to model "particles". These particles can be, whatever we want them to be. People, however, are a little bit more complicated than just some objects moving around.

A human, for example, does not move because of some imaginary nor "social" forces are acting on it, right? You can stop immediately if some brilliant idea strikes your mind. So the "change in the velocity" is almost instantaneous. This means the concept of inertia does not work in the case of human beings.

However, in some cases, this model may work in general and deliver good predictions of certain scenarios. So it's not totally worthless, after all. :-)

Are you aware of this paper: "Avoiding numerical pitfalls in social force models"?

For your paper, I shared with you an overleaf-document, since your tex-file had some issues.

We can discuss it if you like. Just send me an email, and we can organize a meeting.

Best,