מכל מלמדײ השכלתי (duchifat) wrote,
מכל מלמדײ השכלתי

Еще из того ж черновика (английский не вычитан); потом уберу под замок:
The most evident flaw of the Aristotle’s physics, which contradicted the everyday experience, was the problem of the projectile motion, that is, why an arrow or a stone thrown by a person would continue its motion after the force is not applied anymore. Apparently, Aristotle himself believed that this is due to rare air in front of the moving body. However, this could not be considered a satisfactory explanation. The answer was suggested by Jean Buridan (1300-1358), who believed that a special acting force called “impetus” is transferred to the body by the mover, so that the body continues its motion under the action of impetus. The quantitative value of impetus was equal to the mass of the body multiplied by its velocity, making it similar to the modern concept of momentum. Buridan also believed that celestial bodies possessed what he called the circular impetus (angular momentum), which makes them to move with a constant speed along a circular trajectory.

The further development of mechanics was related mostly to astronomical observations. According to the Ptolemaic system, the Sun rotates around the earth. However, it was clear that the trajectories of the Sun and the planets are not perfectly circular, as Aristotle’s physics would suggest for the celestial motion. In his treatise “Almagest,” Claudius Ptolemy (90-168) brought forward the idea of epicycles. The planets were assumed to move in a small circle called an epicycle, which in turn moves along a larger circle called a deferent. With the increasing amount of astronomical observations and data, the geocentric system became quite complex involving large number of epicycles and an even more controversial concept of the equant point. The point on the deferent moves with a constant angular velocity with respect to the equant and not the center of the deferent, which was in contradiction with the Aristotle’s ideal uniform celestial rotation.

The dichotomy between the circular “celestial” motion and straightforward “terrestrial” motion existed until the Persian astronomer Nasir al-Din al-Tusi (1201-1274) has demonstrated that the straightforward motion can be presented as a superposition of two rotational motions: a small circle rotating inside the larger circle of twice the same radius (Fig. 1.2). This so-called “Tusi couple” could substitute for the concept of equant, and was eventually adopted by Nicolaus Copernicus (1473-1543) in his revolutionary heliocentric system (Veselovsky, 1973). Historians of astronomy hypothesized that Copernicus could be aware of the Tusi’s result (Saliba, 1996). Several possible ways of how this result to the European science have been considered, including through the works of Byzantine Greek scientists, Proclus Lycaeus (412-487), Nicole Oresme (1320-1382) or Abner of Burgos (1270-1347). It is noted, also that a crankshaft or crank-slider mechanism converting reciprocating linear motion into rotation, was known to the Romans at least since the 3rd century. This mechanism essentially provides the same function as the Tusi couple. Despite that a satisfactory engineering solution for the conversion of the rotational motion into straight was not invented until James Watt’s invention of the straight-line linkage mechanism for his steam engine (Norton, 2011).

The Copernican system and new observations made the main impact on the development of mechanics in the 17th century. Johannes Kepler (1571-1630) used the astronomical data obtained by Tycho Brahe (1546-1601) to formulate his laws of planetary motion and found that the planetary orbits are elliptical. Galileo Galilei (1564-1642) conducted both astronomical and mechanical studies. He formulated what is called now Galileo’s Principle of Inertia (GPI): “A body moving on a level surface will continue in the same direction at constant speed unless disturbed.” Galileo also recognized the importance of the friction force. Galileo was the first who found that the distance traveled by a body under the action of force is proportional to the square of time, although apparently some earlier authors such as Nicole Oresme have suggested this as well. Galileo also introduced the idea of inertia “force” as well as the idea of frictional force, which in many practical circumstances prevents bodies from their inertial motion with a constant velocity. This was a radical enhancement of the idea the force (the cause of action) as it was understood in Aristotle’s physics. Although the philosophical concepts of “inertia” and “impetus” were discussed yet by John Philoponus (490-570), Jean Buridan (1300-1358), and possibly even by Chinese philosopher Mo Tzi (470-391 BC) and by Avicenna (980-1037), only the GPI contained a clear formulation of this idea (Fig. 1.3). Thus the problem of inertia as a fundamental force of nature found a satisfactory resolution.

As far as friction, another fundamental force from the Aristotle’s physics, the situation was different. After the discovery of inertia, it was realized that the velocity of motion is not proportional to the applied force and, therefore, friction is not proportional to the velocity. Instead, the new concept of the friction force and its proportionality to the applied normal load was suggested by Leonardo da Vinci (1452–1519), who believed that the friction force is equal to the quarter of the normal load. In a clearer way it was proposed by Guillaume Amontons (1663–1705) and later by Charles-Augustin de Coulomb (1736-1806) who formulated the laws of friction stating that the friction force is proportional to the normal load and does not depend on the area of contact, and it is almost independent of the sliding velocity (Truesdell, 1968, 1987).

. . . .

In the preceding sections, we reviewed the development of fundamental concepts of mechanics and showed that the friction force was originally viewed as fundamental as the inertia force. Furthermore, these two forces could not be considered without each other, since friction is what prevents the inertial motion in Galileo’s mechanics. The lack of attention to the friction force in the Aristotle’s physics was due to his misunderstanding of inertia. However, after the problem of inertia was solved, friction did not receive the status of a fundamental force of nature. This is because the available experimental data and conceptual understanding of the friction mechanisms did not allow for such understanding.

В двух словах, я считаю, что в аристотелевской физике трение -- практически такая же фундаментальная сила, как инерция. Две эти силы невозможны друг без друга (грубо говоря, с инерцией без трения ничто никогда не остановится, с трением без инерции не сдвинeтся). Проблема инерции была разрешана усилиями Филопона, Буридана (который с ослом, да) и других, предложивших идею импетуса и живой силы, и окончательно - Галилеем и Ньютоном. Трение же, увы, не получило стaтуса фундаментальной силы природы, потому что разрозненные эмпирические данные в XVII-XIX вв этому не способствовали. И только в наше время появилась возможность связать проявления трения со вторым началом термодинамики (фундаментальным законом природы).

PS, Из всей околонаучной деятельности эпохи cxоластов и Возрoждения наиболее поразительны, по-моему, Оксфордские Калькуляторы. Именно они (а не Ампер, как учат наши учебники) предложили разделение на динамику и кинематику. Они же открыли многое другое. И вот как-то в наше время полузабыты.
Tags: mechanics

  • (no subject)

    На мой взгляд (это я все про трактат Аркадьева думаю), бесконечность возникает не в языке (с его потенциальной возможностью бесконечной рекурсии) а…

  • (no subject)

    Правильно ли я понимаю, что слово "Европа" происходит от финикийского слова для Запада, однокоренного с эрэв, маарав, Магриб и т.п.?

  • (no subject)

    Сформулирую все-таки мнение о трактате Аркадьева. Он заявляет, что сущность человека состоит "в конфликте между языком и доязыковой тенью…

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