Question

i have to write a survey paper on the history of a dynamics related concept, tool, application, or mechanism. i am struggling to find good topics. please help me by suggesting some topics

Answer 1

This article describes a few key points in the development of the field of dynamics. It begins with a brief overview of dynamics’ origins in Ancient Greece, and progresses through the Middle {Ages and the Renaissance, stopping at the times, places, and people that the author considers most relevant. Following that, it summarises the appearance of the Principia, and proceeds to explain its development into what we now call Classical Mechanics.
It should be clear that the contents are not new: they are well known in many fields and have been for many years. They are presented to the control community in the hope that knowledge of, and interest in, the history of science might be improved. Any contributions solely in bringing the subject to an audience that is perhaps generally unacquainted with it. Not only are the contents not new, they are also by no means complete or comprehensive. With those caveats, the author hopes that some of the intended audience might find value in what is presented.
Newton discovered universal gravitation and completed the formal enunciation of the mechanical principles now generally accepted. Since his time no essentially new principle has been stated. All that has been accomplished in mechanics since his day has been a deductive, formal, and mathematical development of mechanics on the basis of Newton’s Laws.

The sentiments expressed by Mach are broadly in line with the opinions of many in academia. The popularity of a belief does not allow us to conclude whether
it is factual or not.
The motivation for writing this paper stems from the sentiments of the great physicist, mathematician, historian of science, and polemicist, Clifford Truesdell2. In his essay A Program toward Rediscovering the Rational Mechanics of the Age of Reason, he wrote:

The scientists, in so far as they take any note of history at all, not only have shared the historians’ neglect of the later [i.e., after Newton] mathematical development of mechanics but also, in the main, have ignored what the historians have learned about the earlier periods and have rested content with Mach’s whole view or a rudimentary abstract of it.

Whether reading a textbook on robotics, marine engineering, aerospace engineering or, indeed, on mechanics itself, the statement above is too often applicable. Discussions of dynamics almost invariably begin by citing the work of Newton (1687) in his Principia, and seldom proceed further than this opus. It is as if classical mechanics arose from the genius of Newton alone.
This hagiography does a great disservice to at least four parties: firstly, to the scholars whose works predate Newton; secondly, to Newton’s contemporaries and successors, who actually synthesised the dynamics that we know and apply today; thirdly, to the present {day students who desire an accurate history of dynamics; and fourthly to Newton himself, whose memory is sullied by the misrepresentation of his work.
This neglect leads us to question why this history is being contemplated here. The problem is that the history of science, a large and growing field, seems to filter little of its knowledge to the practitioners of science. Scientific careers can be built on advanced topics with absolutely no concept of what lies in the foundations. The history of a science is vital to a humble understanding of that science.
Awkwardly, the history of a science can only really be grasped and analyzed after the subject itself is sufficiently well understood. However, once that science is understood and a university degree comes to its end, there is no drive to put the learning into a historical perspective. A modern engineering degree is then more like an advanced trade school diploma than the higher form of learning and understanding that it ought to be, and that it used to be.
A cursory and often inaccurate glance at history seems sufficient nowadays, but should it be? The development of dynamics is a much longer, halting and laborious story that neither began nor ended with Isaac Newton.

Sir Isaac Newton

Sir Isaac Newton (1643-1728), made contributions to virtually every area of natural
philosophy, mathematics, optics, and astronomy. His monumental publication, Philosophy Naturalis Principia Mathematica, usually called The Principia in short, was published in 1687. It is likely the most influential book in the field of classical mechanics, yet is little read. Its purpose was set forth in its preface:

...mechanics will be the science of motion
resulting from any forces whatsoever, and of
the forces required to produce any motion...

Newton set out to explain phenomena throughout the universe. What lay within was to apply everywhere and to every process. The trajectory taken by a cannonball was to be governed by the same laws which governed the orbits of the planets. As the start of his work, he states his definitions of mass, momentum, inertia, and forces, both through contact and at a distance. He then states his laws:
First Law

Everybody perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it thereon.

Second Law The alteration of motion is proportional to the motive force impressed and is made in the direction of the right line in which that force is impressed.
Third Law To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
It is broadly divided into three books, each of which alone would eclipse almost any other. Books One and Two are titled Of the Motion of Bodies, being split into two exhaustive analyses. The third is titled The System of the World.The first book analyses motions in a void. From his laws, he analyses a multitude of motions, such as elliptic, parabolic and hyperbolic orbits around some focus.He investigates the forces that maintain these, i.e. the centripetal forces. Universal gravitation is introduced. After showing how point masses behave in the void under gravitation, he demonstrates that finite bodies can be treated as such. Kepler’s Laws follow directly.The first book organized and systematized principles,
some of which were at least dimly understood before, but these principles had never been organized together into a system of analysis for application everywhere.The second book sets out to explain motion on Earth, where motion does not occur in a void: he sought the details of motion in resisting media. It is here that Newton departs from his program of deducing physical behavior based on his laws: he finds but little use for them. For example, in all his treatments of fluidic motion, he finds no room to apply his principle of momentum. In contrast, he conjures ingenious hypotheses to explain a myriad of things ranging from projectile motions to the speed of sound in air. This book is a testament to Newton’s towering stature as a mathematician and dynamicist. The second book of the Principia is almost entirely new. The scholium of the first section of it reads:
But, yet, that the resistance of bodies is in
the ratio of the velocity, is more a mathematical hypothesis than a physical one.

This sentiment is applicable to much of the hypotheses in the book. Today it is mostly forgotten. The book is dominated by hypothesis after hypothesis, with Newton displaying his flair for creative solutions: often precise, often an excellent approximation, but also often wrong and today of only historical value. There are veins of gold hidden within. His observation that fluidic resistance is proportional to the square of velocity can be found, as can the first description of internal fluidic friction:
The resistance arising from the want of
lubricity in the parts of a fluid is, cæteris
paribus, proportional to the velocity with
which the parts of the fluid are separated from
each other.
That most of the results were incorrect cannot be a criticism of Newton either as a physicist or mathematician. The contribution of this book is immeasurable. For instance, it constitutes the beginning of fluid dynamics and studied many of its problems for the first time. From his efforts, his contemporaries and successors were gifted with a bridgehead from which to attack these subjects in earnest. A myriad of potential motions through fluids is contemplated. The book is the staging point for hydrodynamics. Newton contemplated which hull form might pass through the water with least resistance, introducing an optimization problem that found application throughout the 19thcentury.

The third book set forth his solutions to problems in celestial dynamics, with great success. Kepler’s Laws of Planetary Motion had resulted from Newton’s own, and he performed exhaustive analyses of the Solar System. The deficiencies in the Principia are little discussed.
To the modern scholar, it is often impenetrable and confusing; the language of mathematics has evolved so much since then. A common remark made about the Principia is that Newton strangely resorts to geometrical methods instead of his own calculus. Newton does not use his notation of fluxions, but even as soon as we arrive at Lemma II of Book I, the notion of calculus is present, if in an unfamiliar form.
For rigid body mechanics, there is no treatment of rotation. Although Newton says that the spinning top does not stop spinning except insofar as it is slowed by air." there is no justification given. His statement appears directly after his statement of the First Law, but this law cannot tell us anything about the spinning top. Newton might have perceived that the top continues topspin, just as it would continue in linear motion if so impelled, but it is not possible to explain the spinning top using what is within the Principia. There is certainly no treatment of angular momentum. The motion of a rigid body cannot be described by the methods given in the Principia.
There is no treatment of flexible bodies, such as the catenary curve or the vibrating string, nor is there any analysis of the finite body pendulum. No equations of motion appear for systems of more than two free masses, or one constrained. A prime example of the field’s infancy is the three{body problem. Newton attempted to solve this problem, but the contents of the Principia are insufficient to do so. He devised insightful approximations and valid inequalities, but the three{ body problem was insoluble from his principles. His talent in this area is evident, as his work would not be surpassed until the mid{18th century by the efforts of Euler and Lagrange.

That Newton did not solve all of mechanics’ problems is not a criticism at all, but only part of a clear{ headed appraisal of what he did do. His achievements were monumental. He ought not to be credited with the completion of classical mechanics, but rather its beginnings. In the century following The Principia’s publication, the field of mechanics swelled immensely. For all the credit given to Newton, the world ought to be equally
grateful to his contemporaries and successors, especially Leonhard Euler, the Bernoullis Jakob and John, and Joseph Lagrange. These are the men who synthesized what we now apply today.