Non-linear to linear transformation

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SUMMARY

The discussion focuses on the transformation of non-linear problems into linear ones using coordinate systems, specifically through the example of a point A on a circle rolling along the X-axis, leading to the cycloid equation. By shifting the perspective to point B, the problem simplifies into a linear format. This method is also suggested for application in electromagnetic fields (E-fields and H-fields) between charged points, indicating a potential for broader implications in solving complex problems.

PREREQUISITES
  • Understanding of cycloid equations and their properties
  • Familiarity with coordinate transformations in mathematics
  • Basic knowledge of electromagnetic fields (E-fields and H-fields)
  • Concept of non-linear versus linear problem-solving techniques
NEXT STEPS
  • Research the mathematical principles behind cycloid equations
  • Explore coordinate transformation techniques in physics
  • Study the behavior of E-fields and H-fields in different coordinate systems
  • Investigate applications of linearization methods in solving complex physical problems
USEFUL FOR

Mathematicians, physicists, and engineers interested in problem-solving techniques, particularly those dealing with non-linear dynamics and electromagnetic theory.

tfleming
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take a point A(x_1,y_1) on a circe centre B (x_2, y_2) and allow the circle to roll along an X-axis; now we all know that the cycloid equation to point A is highly non-linear; so now if we take the point B, we find the problem has been converted into a linear problem;

now do this to E-fields and H-fields between charged points; think about it!
 
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so one point is we see a non-linear problem converted into a linear one via our choice of co-ordinates;

can we apply this knowledge to some of most pressing problems??
 

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