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Rigid Bodies In Game Programming Gems ... A Question

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Well, I read through my "Game Programming Gems" (First Edition) sometimes. I'll usually open the book to a random page and read about whatever section I'm in, unless it doesn't interest me much. Last night I happened to flip to the section about rigid bodies. I've never been in college, nor have I taken anything more than a high school geometry class. But I have studied physics myself. And I understand quite a bit of what it's talking about. Until it comes to calculus, that is. I have a friend who has just a little bit longer in college. And he is taking/has taken a calculus course and a physics course. (Or maybe just calculus). Anyhow, my first question is this. There's a part talking about angular velocity. This is what it says: The amount of rotation the body experiences per unit time is called angular velocity (also called rotational velocity), given by: (triangle-thing)'0' lim ------------------- = w (it looks more like a cursive 'w') t->0 (triangle-thing)t If I remember correctly, the "triangle-thing" (LoL) indicates a change. Is that correct. The '0' is the 'theta', which I assume is the angle of rotation, and 't' is the time. Well, my question is what does "lim" stand for. Is it "limit"? My friend was explaining some stuff to me a while back, and he mentioned "limits". Can someone explain to me what this means? It's not that I think I'm going to write my own rigid body implementation or anything. LOL! (Sorry) But I'd like to best understand whatever it is that I'm reading when I do read. I won't read anything other than computer, science, history, and math books. LoL. But can someone please explain to me what a limit is? Or give me some links that will explain more about limits, and calculus altogether? I'd greatly appreciate it. Thanks a lot. Matt U. (BTW, I'm Googling now. I figured that searching anything about plain ol' "Limit" or "Limits" would come up with pretty broad results. But I'll give it a try anyhow.)

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Okay, it appears that I've found the answer. =P It reads like this:

The limit of d0/dt as t (time) approaches zero is 'w', the angular velocity about the center of mass. As 't' gets closer to, but not equal to, zero, then 'w' gets closer to L, the limit.

Well, that wasn't too difficult was it. LoL. Well, thanks everyone. Sorry I posted this question. I didn't Google it first. I apologize. =P

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The question (a bit too late though [smile])

Yeah, lim stands for limit. Since you cannot divide by zero, lim is used when you want to divide by something very very small, but larger than 0 (you can use it for other things, but that's the meaning in this example).

The meaning of the limit you are refering to is simply: if you go a tiny bit forward in time, how much does the angle increase? I.e. what is the speed of the angle.

Gamedev (and general) formating tips

There's some formating tips which you might find useful.

When you do asci art, you can use [code][/code] tags, so it becomes like this:


(triangle-thing)'0'
lim ------------------- = w (it looks more like a cursive 'w')
t->0 (triangle-thing)t


(You can 'Edit' another's post to see the code used in the formatting, which was how I got your limit graphics).

For characters, you can use HTML characters. For instance, the triangle thingy you mention called, 'delta' and can be written:
Δ

like so:

Δ

This is a good page for such codes if you know the name of the character.

I'll say this again because it is very useful, if you see fancy layout in a post, just press 'Edit' on the post and you'll see the formating.

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Okay, thanks a lot. It may have been a little bit late, but it still helped me understand the meaning even more. Thanks.

Yeah, I've been wondering how people do that formatting, as I've never been able to. LoL. But now I know.

Thanks again,
Matt U.

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Take a look at these two main math web-sites:
1. http://en.wikipedia.org/wiki/Limit_(mathematics)
2. http://mathworld.wolfram.com/Limit.html

(Always run a search at wolfram researchs' mathworld web-site and at wikipedia for anything that is math related and new to you!)

Also, Google linked me to these three web-sites which I've found extremely helpful (amongst thousands of other good web-sites):
1. http://www.newton.dep.anl.gov/newton/askasci/1995/math/MATH128.HTM
2. http://www.coolmath.com/limit1.htm
3. http://tutorial.math.lamar.edu/AllBrowsers/2413/Limits.asp

By any means, when you don't know where to look for something on the internet - USE GOOGLE! It's your best friend when it comes to the internet!

(In relation to your needs, use the keywords "math", "limit", "limits", "tutorial", "explanation" in any combination in any search engine.)

Yours greatly, Arie.

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