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The controversy was ostensibly over what gets to be the "true quantity of motion", momentum or vis viva (kinetic energy), with Newton and Leibniz on the opposing sides. While there was some philosophical angle at first, a "skillful attack by Leibniz against an inadequate concept, $m|v|$, and its description of the world", it quickly deteriorated into a ...
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Let me clarify first that there are deep conceptual issues with what $E=mc^2$ means, and what it means to verify it. That energy contributes to inertial mass was known before Einstein. In 1900 Poincare showed that electromagnetic field has momentum, hence effectively mass, and implicitly gave it as $E/c^2$. Austrian physicist Hasenöhrl even wrote explicitly $...
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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 planets, were moving on their own steam, pardon, divine nature, and uniformly along circles at that. Early mathematical astronomers accepted this conviction to such ...
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Gaspard-Gustave Coriolis and Jean-Victor Poncelet used the name "quantité de travail" (quantity of work) and "travail mécanique" (mechanical work) to denote the kinetic energy. I guess that this (the term "travail") could be the origin of the symbol $T$. See at the end of https://en.wikipedia.org/wiki/Vis_viva
(Be patient for my superficiality, I am very ...
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I suspect what you really are after is the electron's mass, since we can then "easily" get its energy via an obscure :-) equation developed by some fellow named Einstein.
The path thru measuring the charge-to-mass ratio, followed by some famous oil-drop experiments, is discussed pretty well in a physics.SE page.
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According to the OED, Clausius coined the German word "virial" (from vīs force, strength):
a. In Clausius' kinetic theorem of gases: (see quots.). virial theorem, the theorem that for a steady-state system of particles obeying an inverse square law of force, the time-average of the kinetic energy equals the time-average of the virial; or equivalently, ...
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You can see :
Agamenon Oliveira, A History of the Work Concept: From Physics to Economics, Springer (2014).
Also interesting :
Danilo Capecchi, History of Virtual Work Laws: A History of Mechanics Prospective, Birkhauser (2012).
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I’m pretty sure Lagrange started this, in Méchanique analitique (1788, p. 224; 1809, p. 263; 1811, p. 311; 1815, p. 2): his predecessors mostly worked with the vis viva ($=2T$) instead.
(As to why he chose the letter $T$, no idea. Words like kinetic, energy, work, appeared only later.)
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I must put up a clarifying answer. They groped towards different concepts and talked past each other, in the modern perspective.
Much of what we call Newtonian mechanics is due to Euler, who called it such in his early papers on the topic, but Euler wrote after the controversy. (See Truesdell)
The problem is, as is clearly seen from the primary texts of ...
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("How did Huygens derive the conservation law for of kinetic energy?")
Huygens in 'The Motion of Colliding Bodies' (English translation) contributed ingenious reasoning, mathematics and thought-experiments based on physical assumptions.
But this work was all about the collisions of a particular kind of body -- supposed and idealized at some distance away ...
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The "mathematics" was a combination of experiments with falling bodies, imaginative thought experiments, common sense, and geometric reasoning. Part of it is explained in the book. Galileo found that $v^2$ at the time of impact is proportional to $h$. Torricelli argued that when two bodies are linked together and freely move, but only in a vertical plane, ...
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There are several themes in Huygens' unpublished paper De motu corporum ex percussione ("On the motion of bodies out of collisions"), but maybe the most significant is that he frequently investigates a specific or extreme case (where some factor is zero, one, or infinity) first, and then guesses about a general case which might have those at its boundary. ...
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In theory, relativistic mass was preceded by the "electromagnetic mass" introduced by J.J. Thomson in 1881, and further developed by Heaviside (1888), Searle (1897), Poincaré (1900), Abraham (1902), Lorentz (1904).
https://en.wikipedia.org/wiki/Electromagnetic_mass
In practice, the first experiments precise enough to measure such effects were conducted by ...
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There is a second sentence to the quote:"The energy of the universe is constant. The entropy of the universe is increasing". The conservation of energy law. The second law of thermodynamics. The quote became famous because from the conjuction of the two conclusion about the heat death of the universe appears to follow. The idea was expressed earlier by ...
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Newton wrote the Principia in 1684-1686. At that time, he would not have expected any reader in Europe (with the possible exception of a few friends) to have known the method of fluxions (calculus), which he had never published. In order to have his work understood, he needed to write it without using either the techniques or the notation of fluxions. (...
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In Principia Newton presents a picture based on forces rather than energy and momentum, and he did not have the concepts of vector and of mechanical energy at his disposal. Moreover, Newton opposed Leibniz's idea of putting kinetic energy ("vis viva") at the center of dynamics on philosophical grounds, because he considered forces to be more fundamental. ...
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This is a very interesting and complex topic that is far from closed. Here are some of the sources I have found.
Energy the subtle concept, by Jennifer Coopersmith, is probably the book you are looking for. However, if you get interested in more critical accounts, continue reading.
http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780198716747.001....
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It was a side effect of the vis viva controversy described in What was the vis viva controversy, including its philosophical aspects? about what to call the "quantity of motion", momentum (vis mortua, dead force) or kinetic energy (vis viva, living force). Since the conservation of $mv^2$ in elastic collisions led to singling out vis viva as a useful concept ...
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Let us consider the following info on developments prior to 1905.
Before 1905 (The forthcoming of $E = mc^2$)
1881 J. J. Thompson proposed that a charged conductor in motion increases its mass by $\frac{4}{15} e^2/a$
1904 H. A. Lorentz proposed that $m_L = m_0 (1 – v^2/c^2)^{-3/2}$ based on deformable spherical charge.
1904 Hasenöhrl derived an apparent ...
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Albert Einstein was only 26 (the year 1905)when he published the brief, 3-page article that announced the equivalence between mass and energy, known today as E=mc2 .
In the original paper, Einstein uses V instead of c for the speed of light, and L instead of E for energy.
Today's world famous formula is simply explained in words. Anyway, the message is ...
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Actually, Aristotle argued that all bodies have a natural movement and do not need to be pushed to keep moving. The elements earth and water have a natural movement towards the centre of the cosmos, air and fire have a natural upward movement, and aether (the substance of the heavenly bodies) has a natural circular movement. This is all explained in his ...
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