[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 72
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2 Yuri and Vladislav:
While you are talking about the same mathematics (racing the same term from left to right or right to left) your argument looks pure scholasticism.
Vladislav, maybe you as the person who has experience of "non-inertial approach", simply give an example when the assumption about force of inertia (that is using non-inertial system of readout) gives simpler mathematics?
Copernicus won precisely because he proposed a simpler mathematics to describe the apparent motion of celestial bodies.
Personally, I would not claim anything about simpler mathematics. There are times when a new concept does lead to its simplification, but more often the opposite. And even when the mathematics becomes more complex, if the new concept provides a broader, more adequate model of the rationality it wins out.
In this case, the mathematics is absolutely equivalent. Newton's 2nd law is still the basis. The difference is that a new entity has been introduced, which Newton's mechanics does not need. If only to simplify perception - who would object ? However Vladislav argues that with this essence mechanics acquires some new features that Newtonian mechanics did not have. And this, imho, is already too much.
Служит герметичной перегородкой, чтобы давление воздуха в правой части всегда было больше давления в левой, отсюда разные уровни жидкости и как следствие момент сил .
I understand that, I don't understand how it has the strength to resist the F2-F1 pressure, which should drive it counterclockwise relative to the ring. It has to be movable, right?
По поводу силы упругости: Вы не правы - она возникает под воздействием внешних сил - уберите их (внешние силы) и получите, что сила упругости равна нулю - у тела не возникнет нагрузок, то есть и решать нечего: нет внешних сил - тело в покое или равномерном движении в инерциальной системе, что равноценно.
These are not all solutions, there is also hesitation. That is, I was not talking about the case where there was no external force, but about the case where there was a force and then it disappeared.
Your problems are interesting. It always seemed to me that there should be a noticeable element of randomness (or, if you like, chaos). Unless, of course, there are "preset" defects.
Это я понимаю, я не понимаю откуда у неё силы сопротивляться давлению F2-F1, которое должно гнать её против часовой стрелки. Она ведь должна быть подвижной, так?
For example suspend on a magnet, or magnetic liquid again in a magnetic field (this option does not work).Бывает, что новая концепция действительно приводит к ее упрощению, но чаще наоборот. И даже когда математика усложняется, если новая концепция обеспечивает более широкую, более адекватную модель ральности она побеждает.
В данном случае математика абсолютно эквивалентна. В основе все равно 2-й закон Ньютона. Отличие в том, что введена новая сущность, в которой механика Ньютона не нуждается. Если только для упрощения восприятия - кто бы возражал ? Однако Владислав утверждает, что с этой сущностью механика приобретает какие-то новые возможности, которых в ньютоновской механике не было.
Ptolemy's system used a non-inertial frame of reference. And, as they say, before Kepler the results obtained in this system were more accurate, i.e. more adequate.
Of course, it depends on what is meant by mathematical equivalence. Here we can get the same result using both 'front end' and 'efficient' algorithms. By and large, it's really the same maths, but the efficiency of the approaches is different.
I quite admit that for some problems the use of non-inertial reference frames may be more efficient. And Vladislav named problems that are such at the moment. Moreover, according to him, in some cases this approach is (again, at the moment) has no alternative.
1. You are competing and have overtaken the runner in second position. Which position do you now occupy?
2. You have overtaken the last runner, what position are you in now?
3.Mary's father has five daughters: 1. Chacha 2. Cheche 3. Chicha 4. Chocho.
Question: What is the name of the fifth daughter? Think fast.
In this case, equivalence in mathematics means that both approaches are based on Newton's 2nd law equations. That approach adds nothing new to them.
And the discussion is not about the question of the application of non-inertial systems (we are talking about reference systems, aren't we ?). The discussion is about the concept of the force of inertia and the necessity and efficiency of its application in physics. Start here https://www.mql5.com/ru/forum/123519/page64#265150
It seems that you think that Newton's mechanics does not allow the use of non-inertial systems, but Vladislav's mechanics does and therefore has an advantage. I dare to assure you that this is not true. Newton's mechanics allows the use of any frame of reference. Newton's mechanics formalizes the formulation of the problem and, accordingly, the writing of difusions describing the behaviour of the system. You can do this in an inertial reference frame - it is easy, you can do it in a non-inertial one - it is a bit more complicated, you have to correctly take non-inertiality into account. But when the diphires are written down, you can forget about physics altogether and solve a purely mathematical problem. And nobody stops you from moving to any coordinate system, if that system solves it more easily.
Механика Ньютона допускает использование любых систем отсчета. Механика Ньютона формализует постановку задачи и, соответственно, запись дифуров, описывающих поведение системы. Можно делать это в инерциальной системе отсчета - это просто, можно в неинерциальной - это чуть сложнее, нужно корректно учитывать неинерциальность. Но когда дифуры записаны, можно вообще забыть о физике и решать чисто математическую задачу. И никто не мешает тебе переходить в любую систему координат, если в ней эта система решается легче.
That's pretty much what I was going to say :). Only I suggest that the term "force of inertia" may well be necessary when operating in a non-inertial reference frame. The term "Coriolis force" came up
Ну например на магните подвесить, или магнитная жидкость опять же в магнитном поле ( тока этот вариант не работает проверил) .How was it controlled, was there a glass wheel or something? And was the pressure differential really maintained? If, for example, you twist it by hand. And what about friction, how long could it spin after a jolt?