Published on 12, July, 2020
Helllo there,
I always dreamed of becoming a scientist, but I couldn't get into university. Still, I managed to modify the displacement law, which had been troubling me at zero. I hope you enjoy the modification
Introduction
The standard displacement formula, Δx=xf−xi, can result in zero displacement when xf=xi This limitation is particularly problematic in applications such as simulations, numerical analyses, and contexts requiring continuous motion. For instance, in robotics and animation, zero displacement can cause issues with position tracking and visual continuity. To address this challenge, we propose a modified displacement formula designed to ensure non-zero displacement, which is crucial for accurate modeling and simulation.
Methodology
Redefining Initial Position:
To avoid zero displacement, we introduce a small positive constant ϵ\epsilonϵ. The modified initial position xi′ is defined as:
xi′=xf+ϵ
where ϵ is a small value, selected to be contextually appropriate. The displacement formula then becomes:
Δx′=xf−(xf+ϵ)=−ϵ
This modification ensures that the displacement Δx′ is always non-zero, thus preventing zero displacement in scenarios where continuous motion is required.
Ok cool,
It's been a while since I studied maths, and it's nice to have a mathy discussion again
What I'm thinking is in a real world scenario wouldn't zero displacement sometimes happen, sometimes things don't move and so Δx would be zero.
Using that formula we're just looking at 1 dimensional movement, the starting point xi and the end point xf, along an axis, if an object stays still the displacement is zero and that is a valid result.
A constant is just that, a fixed value, what would that be? How would it be calculated? If a constant is added we're just saying that something always moves a fixed amount over, artificially displacing something. Objects don't suddenly move over a fixed amount at all times so not sure how to calculate such a constant.
If we are looking at continuous motion wouldn't the velocity formula work better in this context, where we could say Δx = v. Δt, so displacement = velocity x time.
Yes your modification will stop a zero displacement result but I'm interested to see how the result can be used.
We can use it in many ways..
Benefits of the Modified Formula: