Recent content by Andrea94

Yes specifically the components I am looking for 😌. Thanks for the help!

I think I get it based on spherical coordinate transformation, The first column corresponds to my problem, but I have to add a negative sign because of the way my directions are set-up.

So the only way we have a y-component is if beta != 0 AND alpha != 0, in which case the component along y from the beta part is sin(beta) (because this will be a diagonal vector contributing both to the y component and negatively to the x-component). So I can see the sin(beta) part, but I don't...

On the z-axis it is clearly cos(beta) since that part of the rotation is not influenced by alpha. For the x-axis, I visualize that if alpha=0 then it is -sin(beta) and if alpha != 0 then this is the same as rotating -sin(beta) by cos(alpha). But I cannot figure out the y-axis.

I have been trying to determine an expression for a unit vector in the direction of F for hours now. I think the expression is supposed to look something kind of like this, But I don't understand at all how to arrive at this expression. Any help?

Ohh I see, thanks a lot for the help!

Hm, the only thing I can think of is that if ##k## is optimal and nonzero, then ##g(k+1) + g(k-1) - 2g(k)## is always positive since for optimal ##k## we have ##\Delta g(k) > 0## and ##\Delta g(k-1) < 0##. Is this what you mean?

Still not sure what I'm supposed to see here 😅

What do you mean? The expression you've written is the same thing as $$\Delta g(k) - \Delta g(k-1)$$ but I'm not sure how that is relevant.

Great, thanks! Didn't even think about the fact that I could do each inequality separately.

See attached screenshot. Stumped on this, I'll take anything at this point (hints, solution, etc).

Yes this is a very meaningful point and I'm glad you brought it up, I should probably have mentioned that the author at the end chose precisely a coordinate system that leads to ##\delta=0## and hence eliminating the occurrence of multiple trigonometric functions, just as you say.

Ah that's true! Didn't even think about that, thank you.

I want to solve ##\frac{du^2}{d\theta ^2}+u=\frac{GM}{h^2}## for ##u(\theta)##, where ##\frac{GM}{h^2}=constant##. The given equation is a nonhomogeneous second order linear DE. I begin by solving the associated homogeneous DE with constant coefficients: ##\frac{du^2}{d\theta ^2}+u=0## which...

Fantastic, thank you so much for the reference! I found the book on Google and looked at page 239. Interestingly, I never saw this anywhere in my multivariable calculus course.