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September 12th, 2017, 11:46 AM   #1
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Question Derivative of a 3D vector

Hi all!

I'm studying game physics from this book, and having trouble figuring out how do you calculate derivatives of 3D vectors divided into components.

So if I have a formula like

$\displaystyle \frac{d\overline{G}}{dt}$

where the G is a vector having the X, Y and Z components, how do I calculate that (i.e. implement it in code)?

Thanks in advance!
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September 12th, 2017, 11:59 AM   #2
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what kind of code are we talking about?

FORTRAN? C? Java? Python?

MatLab? Mathematica?

basically if you have a vector of functions just take the derivative of each element of the vector.

$\vec{G} = (x(t), y(t), z(t))$

$\dfrac{d\vec{G}}{dt} = \left(\dfrac{dx}{dt}, \dfrac{dy}{dt}, \dfrac{dz}{dt}\right)$
Thanks from Country Boy and mkkekkonen

Last edited by romsek; September 12th, 2017 at 12:01 PM.
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September 13th, 2017, 06:25 AM   #3
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Thanks for the answer, it clarified the situation a bit... I have to pick up my high school math books and study the concept of derivative some more. I'm not terribly good at math, but programming interests me greatly.

The language I'm using is C#, as it's the language I've used most. The library would be MonoGame.

EDIT: For clarification, is

$\displaystyle \frac{d\overline{G}}{dt}$

the same as $\displaystyle \Delta\overline{G}$ in the time interval $\displaystyle \Delta t$?

Last edited by mkkekkonen; September 13th, 2017 at 06:45 AM. Reason: Follow-up question
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September 13th, 2017, 09:40 AM   #4
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Quote:
Originally Posted by mkkekkonen View Post
EDIT: For clarification, is

$\displaystyle \frac{d\overline{G}}{dt}$

the same as $\displaystyle \Delta\overline{G}$ in the time interval $\displaystyle \Delta t$?
oy... so you don't really know what a derivative is.

Take a look at your book. I'll answer questions but this isn't a tutoring site.
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September 13th, 2017, 10:38 AM   #5
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I do know that it represents the rate of change at a specific point, I'm just not familiar with the $\displaystyle \frac{dx}{dy}$ representation. Thanks anyway.
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September 13th, 2017, 11:02 AM   #6
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Quote:
Originally Posted by mkkekkonen View Post
I do know that it represents the rate of change at a specific point, I'm just not familiar with the $\displaystyle \frac{dx}{dy}$ representation. Thanks anyway.
the derivative is the limit of what you described as $\Delta t \to 0$

specifically

$\dfrac{dx}{dt} = \displaystyle \lim_{\Delta t \to 0} \dfrac{x(t+\Delta t)-x(t)}{\Delta t}$

But this is just it's definition. This formula is rarely used directly outside of homework problems.
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