Non-linear to linear transformation

[tfleming]

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!

 

[tfleming]

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??

 

[tacman]

The concept of transforming a non-linear problem into a linear one is a common technique in mathematics and physics. In the example given, we can see how a circular motion can be transformed into a linear one by allowing the circle to roll along an X-axis. This transformation simplifies the problem and allows for easier analysis and solution.

Similarly, in the study of electromagnetism, we can apply this concept to E-fields and H-fields between charged points. By transforming the non-linear equations into linear ones, we can better understand and predict the behavior of these fields. This can be especially useful when dealing with complex systems or multiple charged points.

Overall, the transformation from non-linear to linear can greatly enhance our understanding and ability to solve problems in various fields of study. It is a powerful tool that should be utilized whenever possible.