Small Rotation about q: How \epsilon \vec{n} \times \vec{q} Works

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Homework Help Overview

The discussion revolves around the interpretation of the expression \(\epsilon \vec{n} \times \vec{q}\) in the context of small rotations in vector mathematics. The subject area includes vector calculus and rotational dynamics.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the meaning of the cross product in relation to small rotations and question how it corresponds to an angle. There is also a discussion about the interpretation of \(\epsilon\) as representing a small amplitude of rotation.

Discussion Status

Some participants have provided insights into the nature of the cross product and its geometric implications, while others are questioning the relationship between the expression and the concept of an angle. Multiple interpretations are being explored without a clear consensus.

Contextual Notes

There is a mention of the need for clarification on the mathematical representation of the cross product in LaTeX, indicating a focus on notation as well as conceptual understanding.

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Homework Statement


My book says that [tex]\epsilon \vec{n} \times \vec{q}[/tex] represents a small rotation about q.
n is an normal vectors
Obviously the cross product is orthogonal to both n and q, but I did not know it corresponded to an angle?
BY the way, how do you make a cross product in tex?

Homework Equations


The Attempt at a Solution

 
Last edited:
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cross product in tex? \times will be fine

the epsilon correspond to the small amplitude of your infinitestimal rotation I think
 
But why does this represents an angle?
 
It doesn't represent an angle. It represents an infinitesimal displacement. A small displacement from a vector q rotated around an axis along n should be perpendicular to both. Hence nxq.
 

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