What Are the Gauss Principle of Less Constraints and Gibbs-Apell Equations?

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Discussion Overview

The discussion revolves around the Gauss principle of less constraints and the Gibbs-Apell equations, focusing on the availability of introductory and accessible literature on these topics within analytical mechanics.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant notes a lack of literature on the Gauss principle of less constraints and Gibbs-Apell equations, referencing Lanczos's work as a rare source.
  • Another participant suggests specific texts, including "A Treatise on Analytical Dynamics" by Pars and "Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems" by Papastavridis, as potential resources.
  • A participant expresses frustration with the notation used for acceleration, specifically criticizing the use of 'f' in the literature.
  • Another participant mentions that Whittaker also uses 'f' for acceleration, implying a historical context regarding notation preferences in early 20th Century British texts.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the availability of literature, as some suggest specific texts while others express dissatisfaction with existing notation. The discussion remains unresolved regarding the adequacy of resources on the topic.

Contextual Notes

Limitations include potential gaps in the literature on the Gauss principle and Gibbs-Apell equations, as well as the subjective nature of notation preferences among different authors.

andresB
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In the usual literature about analytical mechanics, I find very little about the Gauss principle of less constraints and the Gibbs-Apell equations. I think the only treatment I've seen on Gauss is given In Lanczos's The variational principle of mechanics".

So, I'm looking for introductory and readable books and other sources about the topic.
 
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Pars A Treatise on Analytical Dynamics
Papastavridis Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems
 
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Opening Pars after a long time, I just remembered that he writes f for the acceleration. Worst. Notation. Ever.
 
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I looked at Whittaker and he also uses f. So maybe early 20th Century Britain had not been exposed to the wonders of a. He talks briefly about your stuff in Chapter 9.
 
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