Deducir la Matriz de Rotación 2D y Encontrar Ayuda

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Homework Help Overview

The discussion revolves around deducing the 2D rotation matrix, with participants examining a specific article that addresses this topic. The focus is on understanding the separation of the matrix and the trigonometric functions involved.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the use of trigonometric functions in the matrix, particularly the transition from cos(σ + φ) and sin(σ + φ) to cos(σ) and sin(σ). There is uncertainty about the validity of these relationships and whether they imply a mistake in the article.

Discussion Status

There is an ongoing exploration of the assumptions made in the article, with some participants suggesting that a mistake may have been made regarding the trigonometric identities. This has led to deeper analysis of the concepts involved, although no consensus has been reached.

Contextual Notes

Participants are navigating through potential errors in the article and discussing the implications of these errors on their understanding of the rotation matrix. There is a recognition of the complexity of the relationships between the angles involved.

Zipi Damn
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I was trying to deduce the 2D Rotation Matrix and I got frustrated. So, I found this article: Ampliación del Sólido Rígido/ (in Spanish).

rotacic3b3n-vectores.jpg



I don't understand the second line. How does he separate the matrix in two different parts?
Thanks for your time.
 
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Hi

In the matrix product in the second line, the vector (cos(sigma + phi), sin(sigma+phi)) should be (cos(sigma), sin(sigma)), which when multiplied by R is by definition (x,y).

Hope this helps.
 
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I don't know why he uses cos(σ+ψ) and sin(σ+ψ) instead of cos(σ) and sin(σ) when the matrix of the second line is separated.

That would make cos(σ+ψ)=cos(σ). Is this true? I can't see that relation. Because there is no similarity between the triangles formed by the vector (x,y) and the vector (x',y'). So it's imposible the cosine is the same.
 
I think it's just a mistake to be honest. It's definitely not true that cos(sigma + phi)=cos(sigma) for all values of these variables, so I think it's safe to assume it's just a mistake.
 
traxter said:
I think it's just a mistake to be honest. It's definitely not true that cos(sigma + phi)=cos(sigma) for all values of these variables, so I think it's safe to assume it's just a mistake.

Yes, it seems to be a mistake. But this mistake has helped me to analize better these concepts.
Anyway, thank you!
 

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