# Questions tagged [classical-mechanics]

For questions about Classical Mechanics - a branch of Physics involving the study of the motion of macroscopic bodies under the influence of Forces

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### Who stated Impulse-momentum theorem and work-energy theorem for the first time? [closed]

I personally believe that after finding F = ma from Newton's second law we can write acceleration in two ways. First Way a = dv/dt F = m(dv/dt) ........ equation 1 Fdt = mdv after integrating we get, ∫...
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### Origin of the concept of "impulse"

Question: So, I recently looked back into my physics textbook and found the concept of "impulse" there. Now, upon reading the explanation in the textbook and several definitions online, I ...
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### Does Navier-Stokes formulation change over timeline?

In this article write: "the equation was rediscovered or re-derived at least four times, by Cauchy in 1823, by Poisson in 1829, by Saint-Venant in 1837, and by Stokes in 1845" "To ...
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1 vote
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### F = ma -- How was did we come to understand that this compact form expressed what Newton said in words?

My understanding is, Newton in the 17th century did not use this formula but rather said, in words basically that if you apply a force it will cause a mass to accelerate in the direction of that force....
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### Would they have known you can't go faster than light in 1790 [duplicate]

I came across this short: https://www.youtube.com/shorts/LjBaPxutpQo where Brian Cox says the idea of black holes dates back to 1790. It stemmed according to it from escape velocity and that you could ...
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### What was John Cantius' contribution to the theory of impetus?

According to Wikipedia, the theory of impetus, which was a precursor to the modern concepts of inertia and momentum, was developed in the West by Jean Buridan, and further developed by John Cantius (...
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### Hamilton's derivation for the characteristic function in his essay

In Hamilton's "on a general method in dynamics", he starts with varying the function $U$ and writes the equation: $$\delta U=\sum m(\ddot x\delta x+\ddot y\delta y+\ddot z\delta z)$$ Then he ...
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### Did Newton know about non-inertial frames?

When answering a Physics.SE question, I made a claim that Newton realized that $F=ma$ worked in some frames, which are called "inertial frames." Nowadays, we know that there are non-...
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### Reconstruction of Newton's axioms

Hilbert reconstructed Euclid's axioms. Is there an equivalent restructuring of Newton's axioms, or are they considered consistent?
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### How does Legendre transformation in classical mechanics relate to Adrien-Marie Legendre?

I tried to look for the history of Legendre transformation, which transformed Lagrangian mechanics to Hamiltonian mechanics, usually formulated as  \begin{cases} p_i = \frac{\partial L}{\partial v_i}...
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### How the concept of Momentum was discovered?

As we already know that the concept of Momentum was discovered before Newton discovered his laws of motion, but my question is $\rightarrow$ How they discovered the relationship p=mv without knowing ...
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### Are similarities in notation between Hamiltonian mechanics and Box-Jenkins time series forecasting accidental?

The 1833 formalism of Hamiltonian mechanics prescribes phase space coordinates (p,q) as momenta. https://en.wikipedia.org/wiki/Hamiltonian_mechanics The Box-Jenkins method (1970) of time series ...
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### How did Newton, Lagrange, Hamilton and others ideate their mechanical formulations?

What exactly did Lagrange do, historically? This is very relevant but the accepted answer just does similar speculations based on contextual details that I have done. It was mentioned that part of ...
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### Where does motion happen for Galileo?

I have a question from the first two paragraphs of this answer: Newton's idea of absolute space simply appeared as an answer to the following question: What is an inertial system? Saying that an ...
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### What led to people looking at phase spaces?

In basic physics, the emphasis is calculating total forces, and going from that to the position function of the body as a function of time by integration. Now, from this prespective, how did people ...
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### How did Alexis Bouvard calculate the orbits of Jupiter, Saturn and Uranus

In 1821 Alexis Bouvard published a book with tables of the orbits of Jupiter, Saturn and Uranus and future predictions of the orbits. The real orbit of Uranus deviated from the calculations which was ...
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### Archimedes' lever and the concept of work

Do I understand correctly that Archimedes was not familiar with the concept of work and hence attributed mechanical advantage to a lever's ability to create force rather than understanding that the ...
1 vote
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### Book suggestions on Lagrangian and Hamiltonian mechanics?

What are some books that talk about the origins of Lagrangian and Hamiltonian mechanics? I would like to dig deeper into the fundamental approach and the fundamentals of action and its principles.
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### Did William Rowan Hamilton respond to the assertions by Jacobi?

In his 'Vorlesungen über Dynamik', 1842-1843, Jacobi also discusses the papers by William Rowan Hamilton. Jacobi asserted that Hamilton had inadvertendly introduced a superfluous equation, which of ...
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### Does Galilean/Newtonian mechanics reject both consequences of Aristotle's dynamical pseudo-law : $V = F/m$, or only consequence (1)?

Note : my question is not as to whether consequence (2) is correctly derived from Arstotle's "law" ( I think it is the case) but as to whether this consequence is still true in Newtonian ...
1 vote
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### Which physical quantities were used or introduced by Newton?

I have never read his original works, but I would say that he must have used length, volume, time, velocity, acceleration, momentum or force, and maybe (kinetic) energy. Which quantities appeared in ...
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### Before Einstein did people realize about a falling man not feeling weight?

I understand that Einstein was able to draw remarkable conclusions and was set on the path of General relativity when he realized that a falling observer not feeling his own weight. But is it believed ...
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### Motivation of the Hamiltonian formalism

In 1833 Hamilton introduced what today is called the Hamiltonian formalism in classical mechanics. I am wondering what was his motivation. Did he try to solve a specific question?
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### Paradigms in Newtonian physics around 1900

I am thinking about the change from Newtonian mechanics to quantum physics and relativity. I note that we have accepted the words "ultraviolet catastrophe" in connection with the situation ...
1 vote
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### How Galileo could both possibly say that Earth is revolving around the Sun and develop the Galilean relativity?

I always have been curious about this part of the History of Science. To claim that Earth is orbiting the Sun instead of the opposite is equivalent to change one absolute referential (Earth) to ...
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### Were there non-Western models of projectile motion before Galileo?

When I search for the history of projectile motion, I mostly find outlines starting with Aristotle and discussing Ibn Sina, Tartaglia, Galileo, Newton, etc. and perhaps with a few more Europeans in ...
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### Why was the concept of momentum invented in the first place, and what is its history?

Why was the concept of momentum invented in the first place, and is it useful in the different discoveries and equations that came after?
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### What motivated scientists to define quantities at a point?

We know that quantities can be defined at a point. Let's take density for instance. If we take a volume in some quantity of matter and keep on shrinking it to a point where we can assign a uniform ...
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### Parisian scholastics' work on mechanics

I was reading the Compendium of the foundations of classical statistical physics by Jos Uffink where, on p. 4, the following statement is made: In a discussion of the foundations of classical ...
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### Newton's Corollary #1 to the Laws of Motion (Principia)

I'm currently working through selected portions of Newton's Principia, but I'm already stuck in trying to understand his explanation for the first corollary (i.e., Corollary I) to the laws of motion. ...
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### What exactly did Lagrange do, historically?

I'm tying to understand, historically, what lead to Lagrangian mechanics (LM). What did Lagrange actually do? In the time (year 1788), when Lagrange published his work (that we nowadays call "...
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### Upon which incorrect equation of Euler did Sophie Germain rely in her work that won a prix extraordinaire from the Paris Academy of Sciences?

Wikipedia's Sophie Germain; Work in elasticity; Subsequent attempts for the Prize says: Germain had derived the correct differential equation (a special case of the Kirchhoff–Love equation),31 but ...
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### What motivated formulation of the Hamilton-Jacobi equation?

I'm late to the Hamilton-Jacobi equation party and would like to know more about the historical context of its origin. What motivated its construction/discovery? What were its affordances over other ...
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### Did the concept of mass exist before Newton?

I have been learning Newton's laws, and I am confused about the different formulations of the laws, the definitions of the quantities in the modern version, and the definitions of the quantities ...
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### Are there any direct comments by Isaac Newton on Leibniz's living force / vis-viva?

The living force or the vis-viva is a quantity usually attributed to Leibniz (although there were a few other people who identified it as a conserved quantity in certain collisions earlier). Many ...
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### Einstein's Objection to Drude Model

In Walter Isaacson's Biography of Einstein, it is stated that the young Einstein was developing his own ideas in Statistical Physics and Thermodynamics and he had found some error in Drude's model for ...
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### What led to the formula $W=\vec{F} \cdot \overrightarrow{d s}$? [closed]

For me the concept of energy in physics is the least intuitive one as in all the books on Physics that I have read so far. The concept of energy have been the least intuitive one as I cannot ...
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### Galileo's discovery of the independence of motion

It is well-known that Galileo was the first one to state that motions in different dimensions (or components) are independent of one another. Where is this in Galileo's writings?
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### Who first defined velocity and acceleration?

I'm asking who was the first to use and define velocity and acceleration in the modern, now standard way, with velocity being the first derivative of position and acceleration being the second ...
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### History of rotational / rigid body mechanics

In teaching introductory mechanics classes, I like to give my students a much-abridged sketch of some history of mechanics, starting with Aristotle and ending with Galileo and Newton. Most of the ...
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### Why do I , J and K in mechanics represent X , Y and Z in maths?

Why are letters $i$, $j$, and $k$ used for axes names in mechanics while letters $x$ , $y$ and $z$ are used in mathematics? Why these dimensions weren't called A, B and C or F, G and H?
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### Gravity before Aristotle

In this wiki article, the history of gravity starts with Aristotle. However, what were the ideas about Earth's gravity and motion of planets before Aristotle?
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### When were the SUVAT equations derived for the first time?

It's one of the first things learned in Physics. However, what's the history behind deriving the SUVAT equations? And, there were other equivalent equations used before SUVAT came into the curriculum?
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### Why did Galileo express himself in terms of ratios when describing laws of accelerated motion?

I opened the same question on Physics Stack Exchange, but it seems more suited for this site. I've been reading about Galileo's experiment with inclined planes, and he ends up saying something along ...
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### Why isn't the history of mechanics dated from Archimedes time?

It's often said - and more often written - and perhaps, even more spoken of - that modern physics began with Galileo due to his application of mathematics to motion. This is the position taken by ...
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### kinetic energy formula written as mv^2

I stumbled across the following quote and couldn't understand how one wouldn't use the factor of 1/2 without completely disrupting the work-energy principle. Though, informal, energy is defined as the ...
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### Why do we use $U$ for potential energy in classical mechanics?

I am unaware if someone has asked this before, but I am studying classical mechanics and I don’t know why do we use $U$ for potential energy. I have read that Rankine used it first, but I can’t find ...
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### Who made the first derivation of the angle to maximise projectile range, which turned out to be wrong?

I remember hearing once that the first "proof" that the angle to maximise projectile range gave the correct answer, 45 degrees, but was later found that the proof was wrong. I can't remember ...
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In Thm. 4, Prop. 4 of Galileo's 'Two New Sciences' (pg. 187, Crew Translation), Galileo says the following: "From a single point $B$ draw the planes $BA$ and $BC$, having the same length but ...