Second order differential equation of the pendulum system












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$begingroup$


Who was the first to derive second order differential equation representing a simple case pendulum? (Galileo, Newton, Huygens, Leibniz or someone else)?



$ddottheta = sin(theta)$



I personally suspect Huygens, however I do not have a proof.






ordinary-differential-equations







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  • 1




    $begingroup$
    Henry Kater in 1817.
    $endgroup$
    – JCH
    Jan 1 at 19:53






  • 1




    $begingroup$
    @JCH: Source? Surely it must have been known much earlier than that, given that Newton and Huygens studied pendula already in the 17th century.
    $endgroup$
    – Hans Lundmark
    Jan 2 at 11:15






  • 1




    $begingroup$
    Judging from en.wikipedia.org/wiki/Christiaan_Huygens#Pendulums, it seems Huygens didn't quite get to the equation for the simple pendulum. But I'm thinking that it must at least have been known to people like Euler and Lagrange in the 18th century.
    $endgroup$
    – Hans Lundmark
    Jan 2 at 11:19










  • $begingroup$
    I also have to consider Robert Hooke who was the first to study conical pendulum.
    $endgroup$
    – Aschoolar
    Jan 2 at 14:16
















1












$begingroup$


Who was the first to derive second order differential equation representing a simple case pendulum? (Galileo, Newton, Huygens, Leibniz or someone else)?



$ddottheta = sin(theta)$



I personally suspect Huygens, however I do not have a proof.






ordinary-differential-equations







share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    Henry Kater in 1817.
    $endgroup$
    – JCH
    Jan 1 at 19:53






  • 1




    $begingroup$
    @JCH: Source? Surely it must have been known much earlier than that, given that Newton and Huygens studied pendula already in the 17th century.
    $endgroup$
    – Hans Lundmark
    Jan 2 at 11:15






  • 1




    $begingroup$
    Judging from en.wikipedia.org/wiki/Christiaan_Huygens#Pendulums, it seems Huygens didn't quite get to the equation for the simple pendulum. But I'm thinking that it must at least have been known to people like Euler and Lagrange in the 18th century.
    $endgroup$
    – Hans Lundmark
    Jan 2 at 11:19










  • $begingroup$
    I also have to consider Robert Hooke who was the first to study conical pendulum.
    $endgroup$
    – Aschoolar
    Jan 2 at 14:16














1












1








1





$begingroup$


Who was the first to derive second order differential equation representing a simple case pendulum? (Galileo, Newton, Huygens, Leibniz or someone else)?



$ddottheta = sin(theta)$



I personally suspect Huygens, however I do not have a proof.






ordinary-differential-equations







share|cite|improve this question









$endgroup$




Who was the first to derive second order differential equation representing a simple case pendulum? (Galileo, Newton, Huygens, Leibniz or someone else)?



$ddottheta = sin(theta)$



I personally suspect Huygens, however I do not have a proof.






ordinary-differential-equations




ordinary-differential-equations






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 1 at 18:00









AschoolarAschoolar

1991110




1991110








  • 1




    $begingroup$
    Henry Kater in 1817.
    $endgroup$
    – JCH
    Jan 1 at 19:53






  • 1




    $begingroup$
    @JCH: Source? Surely it must have been known much earlier than that, given that Newton and Huygens studied pendula already in the 17th century.
    $endgroup$
    – Hans Lundmark
    Jan 2 at 11:15






  • 1




    $begingroup$
    Judging from en.wikipedia.org/wiki/Christiaan_Huygens#Pendulums, it seems Huygens didn't quite get to the equation for the simple pendulum. But I'm thinking that it must at least have been known to people like Euler and Lagrange in the 18th century.
    $endgroup$
    – Hans Lundmark
    Jan 2 at 11:19










  • $begingroup$
    I also have to consider Robert Hooke who was the first to study conical pendulum.
    $endgroup$
    – Aschoolar
    Jan 2 at 14:16














  • 1




    $begingroup$
    Henry Kater in 1817.
    $endgroup$
    – JCH
    Jan 1 at 19:53






  • 1




    $begingroup$
    @JCH: Source? Surely it must have been known much earlier than that, given that Newton and Huygens studied pendula already in the 17th century.
    $endgroup$
    – Hans Lundmark
    Jan 2 at 11:15






  • 1




    $begingroup$
    Judging from en.wikipedia.org/wiki/Christiaan_Huygens#Pendulums, it seems Huygens didn't quite get to the equation for the simple pendulum. But I'm thinking that it must at least have been known to people like Euler and Lagrange in the 18th century.
    $endgroup$
    – Hans Lundmark
    Jan 2 at 11:19










  • $begingroup$
    I also have to consider Robert Hooke who was the first to study conical pendulum.
    $endgroup$
    – Aschoolar
    Jan 2 at 14:16








1




1




$begingroup$
Henry Kater in 1817.
$endgroup$
– JCH
Jan 1 at 19:53




$begingroup$
Henry Kater in 1817.
$endgroup$
– JCH
Jan 1 at 19:53




1




1




$begingroup$
@JCH: Source? Surely it must have been known much earlier than that, given that Newton and Huygens studied pendula already in the 17th century.
$endgroup$
– Hans Lundmark
Jan 2 at 11:15




$begingroup$
@JCH: Source? Surely it must have been known much earlier than that, given that Newton and Huygens studied pendula already in the 17th century.
$endgroup$
– Hans Lundmark
Jan 2 at 11:15




1




1




$begingroup$
Judging from en.wikipedia.org/wiki/Christiaan_Huygens#Pendulums, it seems Huygens didn't quite get to the equation for the simple pendulum. But I'm thinking that it must at least have been known to people like Euler and Lagrange in the 18th century.
$endgroup$
– Hans Lundmark
Jan 2 at 11:19




$begingroup$
Judging from en.wikipedia.org/wiki/Christiaan_Huygens#Pendulums, it seems Huygens didn't quite get to the equation for the simple pendulum. But I'm thinking that it must at least have been known to people like Euler and Lagrange in the 18th century.
$endgroup$
– Hans Lundmark
Jan 2 at 11:19












$begingroup$
I also have to consider Robert Hooke who was the first to study conical pendulum.
$endgroup$
– Aschoolar
Jan 2 at 14:16




$begingroup$
I also have to consider Robert Hooke who was the first to study conical pendulum.
$endgroup$
– Aschoolar
Jan 2 at 14:16










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