equations:hamiltons_equations
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equations:hamiltons_equations [2018/05/06 13:52] jakobadmin [Intuitive] |
equations:hamiltons_equations [2019/02/12 15:21] (current) 129.13.36.189 [Why is it interesting?] |
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| This comes at the cost of doubling the size of the system. | This comes at the cost of doubling the size of the system. | ||
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| + | <blockquote>[E]verybody loves Hamilton’s equations: there are just two, and they summarize the entire essence of classical mechanics. | ||
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| + | <cite>[[https://johncarlosbaez.wordpress.com/2012/01/19/classical-mechanics-versus-thermodynamics-part-1/|John Baez]]</cite></blockquote> | ||
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| + | <blockquote>You get equations like Hamilton's whenever a system *extremizes something subject to constraints*. A moving particle minimizes action; a box of gas maximizes entropy. <cite>[[https://twitter.com/johncarlosbaez/status/1065715514381557761|John Baez]]</cite></blockquote> | ||
| <tabbox Origin> | <tabbox Origin> | ||
| - | "Hamilton’s equations and the [[equations:maxwell_relations|Maxwell relations]]—are mathematically just the same. They both say simply that partial derivatives commute." See https://johncarlosbaez.wordpress.com/2012/01/19/classical-mechanics-versus-thermodynamics-part-1/ | + | "Hamilton’s equations and the [[formulas:maxwell_relations|Maxwell relations]]—are mathematically just the same. They both say simply that partial derivatives commute." See https://johncarlosbaez.wordpress.com/2012/01/19/classical-mechanics-versus-thermodynamics-part-1/ |
| and https://johncarlosbaez.wordpress.com/2012/01/23/classical-mechanics-versus-thermodynamics-part-2/ | and https://johncarlosbaez.wordpress.com/2012/01/23/classical-mechanics-versus-thermodynamics-part-2/ | ||
equations/hamiltons_equations.1525607531.txt.gz · Last modified: 2018/05/06 11:52 (external edit)
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