Notation for generalized coordinates

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Discussion Overview

The discussion centers around the notation used for generalized coordinates in the context of Lagrangian mechanics, specifically the use of symbols such as rk and qj. Participants explore whether these notations are interchangeable and the implications of using different symbols.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions whether rk and qj represent the same concept in Lagrange equations and if the choice of notation matters.
  • Another participant argues that notation is largely conventional and emphasizes the importance of clarity in specifying what notation is being used.
  • A participant notes that Wikipedia uses both notations in the same article, prompting a question about whether this indicates differing author preferences or if rk has a distinct meaning.
  • Some participants clarify that "r" is used for position vectors rather than generalized coordinates, while also acknowledging that position vector components can serve as generalized coordinates.
  • There is a suggestion that the article discusses transitioning to a more general case by defining generalized coordinates as q.

Areas of Agreement / Disagreement

Participants express differing views on the interchangeability of rk and qj, with some asserting that notation is conventional while others seek clarification on specific usages. The discussion remains unresolved regarding the implications of using different notations.

Contextual Notes

There are limitations in the discussion regarding the assumptions behind the notation and the specific contexts in which rk and qj are used. The relationship between position vectors and generalized coordinates is also not fully explored.

Isaac0427
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I have seen both rk and qj both used to represent generalized coordinates in the Lagrange equations. Are these both the same things? Does it matter which you use?
Thanks!
 
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No, what you are calling things are typically completely conventional. You could call energy R, mass x, and the speed of light T and you would have R = xT^2 - nobody would understand you if you did not specify what notation you were using though. The notation I have seen the most is to use q for generalized coordinates, but it really does not matter as long as you specify what you are doing and use a notation which is not inherently confusing.
 
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Orodruin said:
No, what you are calling things are typically completely conventional. You could call energy R, mass x, and the speed of light T and you would have R = xT^2 - nobody would understand you if you did not specify what notation you were using though. The notation I have seen the most is to use q for generalized coordinates, but it really does not matter as long as you specify what you are doing and use a notation which is not inherently confusing.
Ok, but Wikipedia used both in the same article (even in the same equation). Are these just differing authors or is rk different?
 
The components of the position vectors form a possible set of "generalized" coordinates.
So you can write the equations in terms of them.
Have you read the article? The part when they say that you can go to a more general case, by defining generalized coordinates, q?
 

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