Motion of a pendulum with air resistance
Here you are using Reynolds law formula for drag. If you use Stokes law, and consider small amplitudes, you can simplify greatly your formula. See
http://nrich.maths.org/6478/solution
http://nrich.maths.org/content/id/6478/Paul-not%20so%20simple%20pendulum%202.pdf
http://nrich.maths.org/content/id/6478/Ben-Not%20so%20simple%20pendulum%202.pdf
Another interesting paper is
The pendulum - Rich physics from a simple system
by Robert A. Nelson and M. G. Olsson
Am. J. Phys., Vol. 54, No. 2, February 1986
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AlexanderRD
I develop a small personal website using a PHP backed with a PostgreSQL Database. I learnt Python as my first languages and sometimes use it for small projects. In addition I enjoy exploring new languages including esoteric languages to see what they can do. In addition I am studying for a degree in Mathematics so use MATLAB and R for my studies.
Updated on August 01, 2022Comments
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AlexanderRD over 1 year
I am trying to model the motion of a pendulum with air resistance. I have resolved perpendicular to the direction of motion to get this equation where $m$, $g$, $p$, $C_D$ and $A$ are constants: $$mg\sin(θ)-\frac{1}{2} pv^2 C A=ma$$
This can be expressed as the following differential equation $$mg \sin(θ) - \frac{1}{2} p\left(\frac{dθ}{dt}\right)^2 C =m\left(\frac{d^2 θ}{dt^2}\right)$$
How this equation would be solved?
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Bobson Dugnutt over 7 yearsI don't think there are any known solutions - you'll have to solve it numerically.
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Sangchul Lee over 7 yearsI agree with Lovsovs, considering that even the solution for the equation without damping term involves Jacobi theta function.
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Lutz Lehmann over 6 yearsThe friction term always works to slow down, thus should always have a sign opposite the direction, $-CAp|v|v$.
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