Second order differential equation of the pendulum system
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
asked Jan 1 at 18:00
AschoolarAschoolar
1991110
$endgroup$
add a comment |
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
asked Jan 1 at 18:00
AschoolarAschoolar
1991110
$endgroup$
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
add a comment |
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
asked Jan 1 at 18:00
AschoolarAschoolar
1991110
$endgroup$
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
asked Jan 1 at 18:00
AschoolarAschoolar
1991110
asked Jan 1 at 18:00
AschoolarAschoolar
1991110
asked Jan 1 at 18:00
AschoolarAschoolar
1991110
asked Jan 1 at 18:00
AschoolarAschoolar
1991110
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
add a comment |
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
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3058702%2fsecond-order-differential-equation-of-the-pendulum-system%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
draft saved
draft discarded
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3058702%2fsecond-order-differential-equation-of-the-pendulum-system%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
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