Alyosha

1,014 reputation

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	1,014 reputation	bio	website		visits	member for	8 months
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Dec 25	accepted	How is this second form of the Euler-Lagrange equation arrived at?
Dec 24	comment	How is this second form of the Euler-Lagrange equation arrived at? By 'expand the total derivative of the function $F$' do you mean taking the differential: $\frac{dF}{dt}=\frac{d}{dt}(F_q dq+ F_{\dot{q}} d\dot{q}+ F_t dt)$?
Dec 24	comment	How is this second form of the Euler-Lagrange equation arrived at? Wouldn't $\frac{d}{dt}(F-\dot{q}\frac{\partial F}{\partial \dot{q}})=0$ be the conservation of energy, or is $\frac{\partial F}{\partial t}=0$?
Dec 24	asked	How is this second form of the Euler-Lagrange equation arrived at?
Dec 24	accepted	Proving the equality of 2 functions
Dec 24	comment	Proving the equality of 2 functions Thanks- I was going the wrong way, trying to force $h(n)$ out of $g(n,f(n-1))$.
Dec 24	comment	Proving the equality of 2 functions Yes, I condensed notation incorrectly.
Dec 24	revised	Proving the equality of 2 functions deleted 4 characters in body
Dec 24	revised	Proving the equality of 2 functions made more flowing
Dec 24	asked	Proving the equality of 2 functions
Dec 23	comment	Invariants in a second order equation "Orthogonal transformations of $(x,y,z)$ (of which two-dimensional orthogonal transformations of only $x$ and $y$ are a special case) must, at a minimum, preserve the coefficients of the characteristic polynomial of this matrix"- Why is this? (I know only rudimentary linear algebra, but the gist of the rest of the answer makes sense)
Dec 23	revised	Invariants in a second order equation added 3 characters in body
Dec 23	revised	Invariants in a second order equation edited tags
Dec 23	asked	Invariants in a second order equation
Dec 23	comment	Spherical projection Both. I realise it would have been better to make two questions, the latter was more of an afterthought. Both answers helped; I somewhat arbitrarily chose Willie's on account of his links leading to further insights into spherical geometry, even though that wasn't part of the question.
Dec 21	comment	Spherical projection Is the statement in the second quotation provable without using differential geometry?
Dec 21	accepted	Spherical projection
Dec 21	revised	Spherical projection added 180 characters in body
Dec 21	comment	Spherical projection Duly edited, thanks.
Dec 20	accepted	What's the most elegant way of rotating a 3-dimensional co-ordinate system?