21 votes

Did Newton know about non-inertial frames?

TL;DR Yes, but... 1) Inertial frames To say that Newton had the modern conception of even inertial frames (based on the laws of motion), is an overstatement. Theoretically, he did not need them ...
Conifold's user avatar
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19 votes
Accepted

Why did Galileo express himself in terms of ratios when describing laws of accelerated motion?

Galileo followed a venerable tradition of distinguishing numbers, magnitudes of different kinds (lengths, times, areas, etc.) and ratios. This is somewhat analogous to the strictures of modern ...
Conifold's user avatar
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17 votes

Why do I , J and K in mechanics represent X , Y and Z in maths?

This usage of $\mathbf i$, $\mathbf j$, and $\mathbf k$ is not specific to physics. It is also used in mathematics, specifically when teaching linear algebra or multivariable calculus in $\mathbf R^3$ ...
KCd's user avatar
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15 votes
Accepted

Why are canonical coordinates canonical?

Such coordinates were called canonical because they are those in which equations of motion (or, of the hamiltonian flow of a function $H$) take the “canonical form” $$ \frac{dq_i}{dt}=\frac{\partial H}...
Francois Ziegler's user avatar
15 votes
Accepted

Was there early opposition to Newton's mechanics?

There was an opposition. The reasons were mainly philosophical. The main thing which was hard to accept was "action at a distance" through the void space. For example Huygens did not accept ...
Alexandre Eremenko's user avatar
15 votes
Accepted

Who first solved the classical harmonic oscillator?

It was "solved" by Huygens in Horologium Oscillatorum (1673). The scare quotes are there because he never wrote down the equation, and even Newton's laws were not yet explicitly formulated. Huygens ...
Conifold's user avatar
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12 votes
Accepted

How does Legendre transformation in classical mechanics relate to Adrien-Marie Legendre?

The Legendre transform is not tethered to classical mechanics, it is just one application of it, another one is to thermodynamics. Geometrically, it is a general way to re-represent convex functions ...
Conifold's user avatar
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10 votes

Day-to-day tasks of human computers, à la Hidden Figures movie

If you are interested in descriptions of “everyday life” of human computers, here is an excerpt from Stan Ulam’s autobiography, Adventures of a Mathematician (University of California Press, 1991) ...
Margaret Friedland's user avatar
9 votes

Did wave optics anticipate quantum mechanics?

It is more accurate to say that Hamilton anticipated some of the ideas of mathematics and heuristics of quantum mechanics, that would later inspire Schrödinger to produce his formulation of wave ...
Conifold's user avatar
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9 votes

What is the history of the energy concept and its measurement?

The word originated with Aristotle, whose "energeia" and "entelecheia" can roughly be translated as enaction, that which makes matter move, and embodiment, that which makes matter take form, ...
Conifold's user avatar
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9 votes
Accepted

Could scientists of Newton's time have explored the limits of his laws of motion?

At the time of Newton, the scientists could NOT detect any deviation of the Newton's laws from reality. As we know now, the only visible effect of this deviation in the Solar system is the anomalous ...
Alexandre Eremenko's user avatar
9 votes

Who first derived $a =v^2/r$

(a) In answer, first a comment about proportionalities and equalities. Many 17th-century writers, including Huygens and Newton, commonly used proportions rather than equalities, especially to avoid ...
terry-s's user avatar
  • 4,375
9 votes

Foucault pendulum historical question

Yes. Léon Foucault in 1851 published in the Comptes rendus a paper Démonstration physique du mouvement de rotation de la Terre au moyen du pendule detailing his experiment and the mathematical ...
CR Drost's user avatar
  • 406
9 votes

Who made the first derivation of the angle to maximise projectile range, which turned out to be wrong?

This probably refers to Galileo's "derivation" of Tartaglia's observation that cannon balls achieve maximal range when fired at 45°. Tartaglia's theory of projectile motion was wrong, he ...
Conifold's user avatar
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8 votes

Why is calculus missing from Newton's Principia?

Although this question and the answers now have some age to them, I suggest that it's important not to overlook the mythical character of the assumption that underlies this question. The question ...
terry-s's user avatar
  • 4,375
8 votes

How did Newton come up with his formula for gravitational force?

The formula was a commonly discussed hypothesis at that time (Ch. Wren, Hooke, Halley). First attempt to test the formula was made when Newton was a young student in Cambridge: he compared ...
Alexandre Eremenko's user avatar
7 votes

What is the history of the energy concept and its measurement?

There is a chapter "the history of the energy concept" of some 80 pages in Philip Mirowski's book More heat than light which is rather informative. The main point of the story appears to be that ...
sand1's user avatar
  • 2,387
7 votes
Accepted

How did Newton and Kepler (actually) do it?

Goldstine, A History of Numerical Analysis from the 16th through the 19th Century (1977), describes Kepler's approach (p. 47), which may be found in Kepler's Epitome Astronomiae Copernicanae (1618), ...
Michael E2's user avatar
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7 votes
Accepted

Who discovered the normal mode decomposition of coupled oscillators?

Edited. The story is long and complicated. From the mathematical point of view, three statements are involved: A. Eigenvalues of a self-adjoint operator are real and simple, B. There exists an ...
Alexandre Eremenko's user avatar
7 votes
Accepted

What was Liouville's contribution to Liouville's theorem?

Liouville shows (1838, pp. 347-349) that if $x=\phi_t(a)$ is the "complete integral" of an ODE $$ \frac{dx}{dt}=P(t,x) \tag{*} $$ on $\mathbf R^n$ (meaning that $a\in\mathbf R^n$ are $n$ otherwise ...
Francois Ziegler's user avatar
7 votes
Accepted

Who studied kinematics before Galileo? Did Galileo base his kinematic research on the previous work of any other scientist?

Kinematics was distinguished from dynamics by the Merton school (a.k.a. Oxford calculators) of scholastics in 14th century, who worked out kinematics of uniformly accelerated motion. In particular, ...
Conifold's user avatar
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7 votes
Accepted

Are there any direct comments by Isaac Newton on Leibniz's living force / vis-viva?

The controversy was not so much about the tension between vis viva and mechanics, as about what is the "true" quantity of motion, vis viva or momentum, and what is the "metaphysical&...
Conifold's user avatar
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7 votes
Accepted

What exactly did Lagrange do, historically?

I recently came across an article that helped me put Lagrange's work in a very interesting perspective: Author: Craig Fraser (historian of science) Subject: d'Alembert's Traité de Dynamique http://...
Cleonis's user avatar
  • 774
6 votes

Who was the first scientist to suggest that objects can keep moving without applied force?

This depends on which objects you have in mind and who you would call a scientist. There was a broad consensus in the ancient Greek natural philosophy that superlunar objects, like the stars and ...
Conifold's user avatar
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6 votes

Which book gives a thorough understanding on the scientific environment of antiquity?

Not much is really known about general "scientific environment". What we really have is only books and fragments of scientists and references on them in other works. It is commonly acknowledged that ...
Alexandre Eremenko's user avatar
6 votes

Was there early opposition to Newton's mechanics?

Newtonian mechanics was resisted throughout its history, all the way until it was replaced by relativity and quantum mechanics. But the criticism did not so much concern the specifics of his laws of ...
Conifold's user avatar
  • 75.2k
6 votes

The origin of F=ma

The following is not a self-written answer; it's a comment. For obvious reasons here on stackexchange comment space is limited. This comment is large. Descartes struggled at formulating a set of laws ...
Cleonis's user avatar
  • 774
6 votes
Accepted

Who axiomatized classical mechanics in 1949?

Not sure who Machamer and Silberstein had in mind specifically, but, in any case, they are mistaken. Simon published The axioms of Newtonian mechanics in 1947, Hermes Eine Axiomatisierung der ...
Conifold's user avatar
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6 votes

What is the origin of the concept of reduced mass?

The use of reduced mass in spectroscopy goes back to Bohr's planetary model of the atom. Nasri explains the context in his notes on quantum mechanics: "In 1912, Alfred Fowler showed that similar ...
Conifold's user avatar
  • 75.2k
6 votes
Accepted

What is the etymology of "phase space" of a dynamical system?

Here is a direct link to Nolte's Tangled Tale of Phase Space on Physics Today. Big takeaways: the name did not come from Liouville's oft-cited 1838 paper, and Boltzmann used "phase" without &...
Conifold's user avatar
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