September 12th, 2017, 10:46 AM  #1 
Newbie Joined: Sep 2017 From: Finland Posts: 3 Thanks: 0  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! 
September 12th, 2017, 10:59 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 922 
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. $\vec{G} = (x(t), y(t), z(t))$ $\dfrac{d\vec{G}}{dt} = \left(\dfrac{dx}{dt}, \dfrac{dy}{dt}, \dfrac{dz}{dt}\right)$ Last edited by romsek; September 12th, 2017 at 11:01 AM. 
September 13th, 2017, 05:25 AM  #3 
Newbie Joined: Sep 2017 From: Finland Posts: 3 Thanks: 0 
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 05:45 AM. Reason: Followup question 
September 13th, 2017, 08:40 AM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 922  Quote:
Take a look at your book. I'll answer questions but this isn't a tutoring site.  
September 13th, 2017, 09:38 AM  #5 
Newbie Joined: Sep 2017 From: Finland Posts: 3 Thanks: 0 
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.

September 13th, 2017, 10:02 AM  #6  
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 922  Quote:
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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