Can PCA Be Used to Derive Equations of Motion?

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Discussion Overview

The discussion explores the potential application of Principal Component Analysis (PCA) in deriving equations of motion, specifically questioning its relevance to the equation F = kx, which relates force to displacement in a spring system.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires whether PCA can be utilized to derive equations of motion, citing F = kx as an example.
  • Another participant seeks clarification on the meaning of PCA, which is identified as Principal Component Analysis.
  • A participant suggests that PCA could be applied to estimate the constant k in the equation F = kx, proposing that k could be computed as the ratio of the components of the eigenvectors of the covariance matrix.
  • One participant challenges the initial premise by stating that F = kx is not an equation of motion and asks for clarification on the actual problem or goal being addressed.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of PCA to derive equations of motion, with some questioning the relevance of F = kx in this context. The discussion remains unresolved regarding the use of PCA for this purpose.

Contextual Notes

There are unresolved assumptions about the definitions of equations of motion and the specific goals of applying PCA in this context.

touqra
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Was wondering if PCA can be used to find equation of motions, like F = kx.
 
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And PCA means what exactly?
 
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Dr.D said:
And PCA means what exactly?
Principal Component Analysis
 
touqra said:
Was wondering if PCA can be used to find equation of motions, like F = kx.
You mean to estimate the constant k for a spring? You usually use linear regression for that. But you can apply PCA and then compute k as the ratio of the components of the eigenvectors of the covariance matrix.
 
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F=kx is not an equation of motion. What is your actual problem or goal?
 
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