Hey guys, I am looking for a textbook that I can cite as a source for a project, for which I am doing the math on.(adsbygoogle = window.adsbygoogle || []).push({});

I know that for a 22° approximation sinθ=θ and cosθ=1-[itex]\frac{θ^{2}}{2}[/itex]

but for a 5° approximation sinθ=θ but now cosθ=1

and thats all fine and dandy, but I am looking through a paper on an inverted pendulum on a cart, and after solving their system lagrangian, which I have done, when it came down to linearize the final equations, they were saying that the [itex]\dot{\theta}[/itex]^{2}=0

and i believe this comes from the taylor series expansion. Unfortunately I am terrible at taylor series, and I want to know more about this, and what I really need is a textbook that has this information in there, that I can use as a reference source.

if anyone can name a book that will have this information (and hopefully the page that its on as well) if my university library doesn't have it, then hopefully I can find it in some library and if not, hopefully i can download a pdf of it somewhere.

Here is the paper from where I am getting most of this information. It seems to be the most complete. Scroll down to page 12 to see their approximation.

http://web.mit.edu/2.737/www/extra_files/andrew.pdf

thanks guys.

-Robby

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Small angle approximation for (dθ/dt)^2=0

**Physics Forums | Science Articles, Homework Help, Discussion**