• Replies 33 replies
  • Subscribers 43 subscribers
  • Views 1270 views
  • Users 0 members are here
Options
Related
Hints and tips
  • To quote someone's message, first select/highlight the relevant text, and then use the Quote button that appears
  • To "mention" someone, type @ followed by the start of the forum name, and choose from the list; that person will get a notification of being mentioned

Science, A Modified Displacement Formula for Non-Zero Displacements

Noon..

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.

Parents

  • Hello Noon.  It is good to see you back.

    Whilst I have no intention to cause you upset, nor to rain on your parade, I must confess to having some difficulty with the above.

    "a small value, selected to be contextually appropriate" and then added to a formula to "make" it work......does rather fly in the face of how science works.

    As an avid and invested observer of science discoveries (and their methodologies), both past and present, I note that profound breakthroughs are often established because of "otherwise perfect equations" proving to be incorrect in very specific circumstances, or because the results prove to be very, very, very slightly wrong, all of the time, or often.

    To proffer a good and recent example of this - I can refer you to the Henny Penny and Chicken Licken (or Chicken Little if you are American) issue ie, science knew that the centrifugal force throwing our atmosphere away from the planet, and the gravitational force holding our atmosphere down on the planet, couldn't (quite) explain why the sky is as high as it is, from the surface.

    Rather than tweaking the figures to make them work, scientists did long, hard and laborious stuff.......which has recently resulted in the discovery of the Ambipolar magnetic field = a third fundamental planetary force.  How cool is that !!!

    I think continuous motion plus enquiring and curious minds are required in all aspects of science, and I hope your energy and enthusiasm can be maintained forever.  Science needs you.  Science also needs peer review - hence why I have commented above as I have.

    Assuring you of my best intentions towards you and your post above.

    Number.

Reply

  • Hello Noon.  It is good to see you back.

    Whilst I have no intention to cause you upset, nor to rain on your parade, I must confess to having some difficulty with the above.

    "a small value, selected to be contextually appropriate" and then added to a formula to "make" it work......does rather fly in the face of how science works.

    As an avid and invested observer of science discoveries (and their methodologies), both past and present, I note that profound breakthroughs are often established because of "otherwise perfect equations" proving to be incorrect in very specific circumstances, or because the results prove to be very, very, very slightly wrong, all of the time, or often.

    To proffer a good and recent example of this - I can refer you to the Henny Penny and Chicken Licken (or Chicken Little if you are American) issue ie, science knew that the centrifugal force throwing our atmosphere away from the planet, and the gravitational force holding our atmosphere down on the planet, couldn't (quite) explain why the sky is as high as it is, from the surface.

    Rather than tweaking the figures to make them work, scientists did long, hard and laborious stuff.......which has recently resulted in the discovery of the Ambipolar magnetic field = a third fundamental planetary force.  How cool is that !!!

    I think continuous motion plus enquiring and curious minds are required in all aspects of science, and I hope your energy and enthusiasm can be maintained forever.  Science needs you.  Science also needs peer review - hence why I have commented above as I have.

    Assuring you of my best intentions towards you and your post above.

    Number.

Children
  • in reply to Number

    Benefits of the Modified Formula:

    • Non-Zero Displacement: Ensures that even minimal movements are represented, which is essential for applications like robotics where continuous tracking of position is critical. For example, in a robotic arm simulation, ensuring non-zero displacement can help in accurate path planning and obstacle avoidance.
    • Numerical Stability: Helps prevent computational artifacts in simulations where zero displacement could lead to errors or instability. For instance, in numerical fluid dynamics simulations, ensuring non-zero displacement helps maintain stability in iterative calculations.
  • in reply to Number

    Yeah hi I'm sorry for the late reply.. And sorry for not make it .. Scale of the System: ϵ should be much smaller than typical displacements in the system. For example, in a robotic system with displacements on the order of centimeters, ϵ might be set to millimeters or smaller...