Timeline for Momentum a cotangent vector
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 2, 2019 at 22:46 | comment | added | Josh Burby | @roi_saumon, while you do need some norm to define the limit used in the definition, in finite dimensions the choice of norm will not change the Frechet derivative. You might check this question here: math.stackexchange.com/questions/2183053/… | |
| Jun 1, 2019 at 18:26 | comment | added | roi_saumon | @JoshBurby doesn't the Frechet derivative need the concept of norm? | |
| Apr 9, 2019 at 12:27 | comment | added | roi_saumon | @JoshBurby, very interesting, I am starting to learn about this stuff, would you have any good reading recommendations? | |
| Apr 17, 2015 at 14:34 | comment | added | Josh Burby | I should also say that $\mathbf{F}L(v_q)=(DL_q)(v_q)$. | |
| Apr 17, 2015 at 14:27 | comment | added | Josh Burby | @JoséFigueroa-O'Farrill I guess it depends on who you ask. In Abraham and Marsden on p. 219 they say "The transformation $\mathbf{F}L:TQ\rightarrow T^*Q$ thus maps the Lagrange equations into the Hamilton equations. In the literature $\mathbf{F}L$ itself is sometimes called the Legendre transformation (e.g. Sternberg [1964]), while classically the name is usually reserved for the map that takes...[$L$ to $H$]." The Sternberg reference is this I think: amazon.com/Lectures-Differential-Geometry-Chelsea-Publishing/dp/…. | |
| Apr 17, 2015 at 10:29 | comment | added | José Figueroa-O'Farrill | Are you sure that's called the Legendre transform? The Legendre transform relates the Lagragian $L$ to the Hamiltonian $H$. (See, e.g., en.wikipedia.org/wiki/… ) | |
| Apr 17, 2015 at 8:52 | vote | accept | Physicist 2.0 | ||
| Apr 17, 2015 at 4:57 | history | answered | Josh Burby | CC BY-SA 3.0 |