Mixing
Taylor series for with an integral
$begingroup$
I was trying to analyze a large amplitude problem and I got stuck at an equation like this.
$$int_0^T dt=sqrt{frac{l}{2g}}int_{theta_{text{max}}}^{ theta_0} frac{d theta }{ sqrt{costheta - cos theta_{text{max}}}}$$
where everything is constant except the dummy integration variable $t$ and $theta$.
I went online to find a solution but found none so far.
I thought about an infinite Taylor series: Let $y$ be the required function on the right hand side, then $frac{dy}{dtheta}$ will be the known function itself.
$$ y = y(0)+y'(0) + y''(0)ldots$$
I was able to calculate $y(0)$ as an indefinite integral. But there are limits in my integral. I am not sure if this is how I approach the problem.
It seems (?) that I have to find an approximation to an elliptic integral.
integration taylor-expansion
edited Feb 1 at 2:17
Lee David Chung Lin
4,47841242
asked Jan 30 at 9:58
Swap NayakSwap Nayak
72
$endgroup$
add a comment |
$begingroup$
I was trying to analyze a large amplitude problem and I got stuck at an equation like this.
$$int_0^T dt=sqrt{frac{l}{2g}}int_{theta_{text{max}}}^{ theta_0} frac{d theta }{ sqrt{costheta - cos theta_{text{max}}}}$$
where everything is constant except the dummy integration variable $t$ and $theta$.
I went online to find a solution but found none so far.
I thought about an infinite Taylor series: Let $y$ be the required function on the right hand side, then $frac{dy}{dtheta}$ will be the known function itself.
$$ y = y(0)+y'(0) + y''(0)ldots$$
I was able to calculate $y(0)$ as an indefinite integral. But there are limits in my integral. I am not sure if this is how I approach the problem.
It seems (?) that I have to find an approximation to an elliptic integral.
integration taylor-expansion
edited Feb 1 at 2:17
Lee David Chung Lin
4,47841242
asked Jan 30 at 9:58
Swap NayakSwap Nayak
72
$endgroup$
$begingroup$
Have to find an approximation to elliptic integral
$endgroup$
– Swap Nayak
Jan 30 at 16:12
add a comment |
$begingroup$
I was trying to analyze a large amplitude problem and I got stuck at an equation like this.
$$int_0^T dt=sqrt{frac{l}{2g}}int_{theta_{text{max}}}^{ theta_0} frac{d theta }{ sqrt{costheta - cos theta_{text{max}}}}$$
where everything is constant except the dummy integration variable $t$ and $theta$.
I went online to find a solution but found none so far.
I thought about an infinite Taylor series: Let $y$ be the required function on the right hand side, then $frac{dy}{dtheta}$ will be the known function itself.
$$ y = y(0)+y'(0) + y''(0)ldots$$
I was able to calculate $y(0)$ as an indefinite integral. But there are limits in my integral. I am not sure if this is how I approach the problem.
It seems (?) that I have to find an approximation to an elliptic integral.
integration taylor-expansion
edited Feb 1 at 2:17
Lee David Chung Lin
4,47841242
asked Jan 30 at 9:58
Swap NayakSwap Nayak
72
$endgroup$
I was trying to analyze a large amplitude problem and I got stuck at an equation like this.
$$int_0^T dt=sqrt{frac{l}{2g}}int_{theta_{text{max}}}^{ theta_0} frac{d theta }{ sqrt{costheta - cos theta_{text{max}}}}$$
where everything is constant except the dummy integration variable $t$ and $theta$.
I went online to find a solution but found none so far.
I thought about an infinite Taylor series: Let $y$ be the required function on the right hand side, then $frac{dy}{dtheta}$ will be the known function itself.
$$ y = y(0)+y'(0) + y''(0)ldots$$
I was able to calculate $y(0)$ as an indefinite integral. But there are limits in my integral. I am not sure if this is how I approach the problem.
It seems (?) that I have to find an approximation to an elliptic integral.
integration taylor-expansion
integration taylor-expansion
edited Feb 1 at 2:17
Lee David Chung Lin
4,47841242
asked Jan 30 at 9:58
Swap NayakSwap Nayak
72
edited Feb 1 at 2:17
Lee David Chung Lin
4,47841242
asked Jan 30 at 9:58
Swap NayakSwap Nayak
72
edited Feb 1 at 2:17
Lee David Chung Lin
4,47841242
edited Feb 1 at 2:17
Lee David Chung Lin
4,47841242
edited Feb 1 at 2:17
Lee David Chung Lin
4,47841242
4,47841242
asked Jan 30 at 9:58
Swap NayakSwap Nayak
72
asked Jan 30 at 9:58
Swap NayakSwap Nayak
72
asked Jan 30 at 9:58
Swap NayakSwap Nayak
72
72
$begingroup$
Have to find an approximation to elliptic integral
$endgroup$
– Swap Nayak
Jan 30 at 16:12
add a comment |
$begingroup$
Have to find an approximation to elliptic integral
$endgroup$
– Swap Nayak
Jan 30 at 16:12
$begingroup$
Have to find an approximation to elliptic integral
$endgroup$
– Swap Nayak
Jan 30 at 16:12
$begingroup$
Have to find an approximation to elliptic integral
$endgroup$
– Swap Nayak
Jan 30 at 16:12
add a comment |
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$begingroup$
Have to find an approximation to elliptic integral
$endgroup$
– Swap Nayak
Jan 30 at 16:12