- #1
V_Permendur
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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.
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 that's 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
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 that's 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
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