- #1

- 20

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the equations are

the approximations for sin and cos

the equation for Taylor series is ( i don't understand at all )

please help me if you can

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- Thread starter abdooo89
- Start date

- #1

- 20

- 0

the equations are

the approximations for sin and cos

the equation for Taylor series is ( i don't understand at all )

please help me if you can

- #2

- 20

- 0

please help me

- #3

HallsofIvy

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- #4

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taking the Taylor expansion of Eqn ,

i mean equations ( X'1 to X'8 )

after that Taylor expansion has been taken like that

ΔX'={ A0 + ΔA1(ΔX1)+ΔA3(ΔX3)+ΔA11(ΔX1^2))ΔX+B0 Δu → ( xx)

i don't understand equation ( xx = taylor expansion ) , and how can i get A0 , ΔA1 , ΔA3, ΔA11

i mean which rule they used to get A0 , ΔA1 , ΔA3, ΔA11

the complete file has been attached

i mean equations ( X'1 to X'8 )

after that Taylor expansion has been taken like that

ΔX'={ A0 + ΔA1(ΔX1)+ΔA3(ΔX3)+ΔA11(ΔX1^2))ΔX+B0 Δu → ( xx)

i don't understand equation ( xx = taylor expansion ) , and how can i get A0 , ΔA1 , ΔA3, ΔA11

i mean which rule they used to get A0 , ΔA1 , ΔA3, ΔA11

the complete file has been attached

Last edited:

- #5

Ray Vickson

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Homework Helper

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taking the Taylor expansion of Eqn ,

i mean equations ( X'1 to X'8 )

after that Taylor expansion has been taken like that

ΔX'={ A0 + ΔA1(ΔX1)+ΔA3(ΔX3)+ΔA11(ΔX1^2))ΔX+B0 Δu → ( xx)

i don't understand equation ( xx = taylor expansion ) , and how can i get A0 , ΔA1 , ΔA3, ΔA11

i mean which rule they used to get A0 , ΔA1 , ΔA3, ΔA11

the complete file has been attached

The author is NOT (at least initially) using Taylor expansions. He uses approximations of the form

[tex] \sin x_1 \approx p_1(x_1) \equiv \frac{120}{\pi^5} x_1 (x_1 - \pi )\\

\sin 2x_1 \approx p_2(x_1) \equiv \frac{315}{4 \pi^6} (2 x_1 - \pi)(2 x_1 – 2 \pi)\\

\cos x_1 \approx p_3(x_1) \equiv \frac{315}{4 \pi^6} (x_1 + \frac{\pi}{2}) (x_1 - \frac{3 \pi}{2})

[/tex]

etcetera. These are not Taylor expansions; if you read carefully you will see that he makes it clear in the article that he claims he is using a form of least-squares approximation to ##\sin x_1##, etc. However, it appears the author makes some errors; he should have

[tex] \sin x_1 \approx \frac{120}{\pi^5} x_1 (\pi - x_1)[/tex]

with sign opposite sign to what he writes; if you plot the two functions you will see that the approximation is not too bad over the interval ##x \in [0,\pi]##. However, the approximations ##p_2## and ##p_3## are horrible: they do not resemble the functions ##\sin 2x_1## and ##\cos x_1## at all, as you can see by plotting them.

- #6

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First, thank you for your reply, secondly I want to know if this approximations (p2 and p3) are not valid or horrible as you say, what is your advice for me to do?

and why ΔA3 =0

and why ΔA3 =0

Last edited:

- #7

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no one want to help me?

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