Timeline for Curvilinear Coordinates and basis vectors

8 events

when toggle format	what		by	license	comment
Jun 24, 2014 at 9:52	vote	accept	Isomorphic
Jun 23, 2014 at 14:58	history	edited	Qmechanic♦		edited tags
Jun 23, 2014 at 12:57	answer	added	Valter Moretti		timeline score: 4
Jun 23, 2014 at 11:57	comment	added	Selene Routley		The situation is even stronger than @Christoph 's comment implies (although I'm sure he knows this): $\varphi_t$ is bijective throughout some open neighbourhood $\mathcal{U}$ of $\vec{q}$ if and only if the Jacobi matrix is nonsingular throughout $\mathcal{U}$ (the if part is the inverse function theorem, the only if part Christoph's comment).
Jun 23, 2014 at 10:14	comment	added	Christoph		for each $t$, $\mathbf r=\varphi_t(\mathbf q)$; as $\varphi_t$ is bijective, so is the Jacobi matrix $J_{\varphi_t}$ (this follows from differentiating $\varphi_t\circ\varphi_t^{-1}=\mathrm{id}$); the vectors $\frac{\partial\mathbf r}{\partial q_i}$ are just the columns of $J_{\varphi_t}$
S Jun 23, 2014 at 9:38	history	suggested	299792458	CC BY-SA 3.0	Added tags + improved presentation (sharpened and made clearer)
Jun 23, 2014 at 9:28	review	Suggested edits
S Jun 23, 2014 at 9:38
Jun 23, 2014 at 9:14	history	asked	Isomorphic	CC BY-SA 3.0