Galileo and the Equations of Motion


Book Description

This book is intended as a historical and critical study on the origin of the equations of motion as established in Newton's Principia. The central question that it aims to answer is whether it is indeed correct to ascribe to Galileo the inertia principle and the law of falling bodies. In order to accomplish this task, the study begins by considering theories on the motion of bodies from classical antiquity, and especially those of Aristotle. The theories developed during the Middle Ages and the Renaissance are then reviewed, with careful analysis of the contributions of, for example, the Merton and Parisian Schools and Galileo’s immediate predecessors, Tartaglia and Benedetti. Finally, Galileo’s work is examined in detail, starting from the early writings. Excerpts from individual works are presented, to allow the texts to speak for themselves, and then commented upon. The book provides historical evidence both for Galileo's dependence on his forerunners and for the major breakthroughs that he achieved. It will satisfy the curiosity of all who wish to know when and why certain laws have been credited to Galileo.




Galileo Unbound


Book Description

Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.




Math with Bad Drawings


Book Description

A hilarious reeducation in mathematics-full of joy, jokes, and stick figures-that sheds light on the countless practical and wonderful ways that math structures and shapes our world. In Math With Bad Drawings, Ben Orlin reveals to us what math actually is; its myriad uses, its strange symbols, and the wild leaps of logic and faith that define the usually impenetrable work of the mathematician. Truth and knowledge come in multiple forms: colorful drawings, encouraging jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Orlin shows us how to think like a mathematician by teaching us a brand-new game of tic-tac-toe, how to understand an economic crises by rolling a pair of dice, and the mathematical headache that ensues when attempting to build a spherical Death Star. Every discussion in the book is illustrated with Orlin's trademark "bad drawings," which convey his message and insights with perfect pitch and clarity. With 24 chapters covering topics from the electoral college to human genetics to the reasons not to trust statistics, Math with Bad Drawings is a life-changing book for the math-estranged and math-enamored alike.




The Essential Galileo


Book Description

Finocchiaro's new and revised translations have done what the Inquisition could not: they have captured an exceptional range of Galileo's career while also letting him speak--in clear English. No other volume offers more convenient or more reliable access to Galileo's own words, whether on the telescope, the Dialogue, the trial, or the mature theory of motion. --Michael H. Shank, Professor of the History of Science, University of Wisconsin–Madison




Galileo’s Pendulum


Book Description

Bored during Mass at the cathedral in Pisa, the seventeen-year-old Galileo regarded the chandelier swinging overhead--and remarked, to his great surprise, that the lamp took as many beats to complete an arc when hardly moving as when it was swinging widely. Galileo's Pendulum tells the story of what this observation meant, and of its profound consequences for science and technology. The principle of the pendulum's swing--a property called isochronism--marks a simple yet fundamental system in nature, one that ties the rhythm of time to the very existence of matter in the universe. Roger Newton sets the stage for Galileo's discovery with a look at biorhythms in living organisms and at early calendars and clocks--contrivances of nature and culture that, however adequate in their time, did not meet the precise requirements of seventeenth-century science and navigation. Galileo's Pendulum recounts the history of the newly evolving time pieces--from marine chronometers to atomic clocks--based on the pendulum as well as other mechanisms employing the same physical principles, and explains the Newtonian science underlying their function. The book ranges nimbly from the sciences of sound and light to the astonishing intersection of the pendulum's oscillations and quantum theory, resulting in new insight into the make-up of the material universe. Covering topics from the invention of time zones to Isaac Newton's equations of motion, from Pythagoras' theory of musical harmony to Michael Faraday's field theory and the development of quantum electrodynamics, Galileo's Pendulum is an authoritative and engaging tour through time of the most basic all-pervading system in the world. Table of Contents: Preface Introduction 1. Biological Timekeeping: The Body's Rhythms 2. The Calendar: Different Drummers 3. Early Clocks: Home-Made Beats 4. The Pendulum Clock: The Beat of Nature 5. Successors: Ubiquitous Timekeeping 6. Isaac Newton: The Physics of the Pendulum 7. Sound and Light: Oscillations Everywhere 8. The Quantum: Oscillators Make Particles Notes References Index Reviews of this book: The range of things that measure time, from living creatures to atomic clocks, brackets Newton's intriguing narrative of time's connections, in the middle of which stands Galileo's famous discovery about pendulums...Science buffs will delight in the links Newton makes in this readable tour of how humanity marks time. --Gilbert Taylor, Booklist




Chemical Cosmology


Book Description

The composition of the most remote objects brought into view by the Hubble telescope can no longer be reconciled with the nucleogenesis of standard cosmology and the alternative explanation, in terms of the Λ-Cold-Dark-Matter model, has no recognizable chemical basis. A more rational scheme, based on the chemistry and periodicity of atomic matter, opens up an exciting new interpretation of the cosmos in terms of projective geometry and general relativity. The response of atomic structure to environmental pressure predicts non-Doppler cosmical redshifts and equilibrium nucleogenesis by α­-particle addition, in accord with observed periodic variation of nuclear abundance. Inferred cosmic self similarity elucidates the Bode –Titius law, general commensurability in the solar system and the occurrence of quantum phenomena on a cosmic scale. The generalized periodic function involves both matter and anti-matter in an involuted mapping to a closed projective plane. This topology ensures the same symmetrical balance in a chiral universe, wrapped around an achiral vacuum interface, without singularities. A new cosmology emerges, based on the theory of projective relativ­ity, presented here as a translation of Veblen’s original German text. Not only does it provide a unification of gravity, electromagnetism and quantum theory, through gauge invariance, but also supports the solution of the gravitational field equations, obtained by Gödel for a rotating universe. The appearance of an Einstein–Rosen bridge as outlet from a black hole, into conjugate anti-space, accounts for globular clusters, quasars, cosmic radiation, γ-ray bursters, pulsars, radio sources and other re­gions of plasma activity. The effects of a multiply-connected space-time manifold on observa­tions in an Euclidean tangent space are unpredictable and a complete re-assessment of the size and structure of the universe is indicated. The target readership includes scientists, as well as non-scientists – everybody with a scientific or philosophical interest in cosmology and, especially those cosmologists and mathematicians with the ability to recast the crude ideas presented here into appropriate mathematical models.




Einstein For Dummies


Book Description

Genius demystified, the Dummies way! In 1905, Albert Einstein revolutionized modern physics with his theory of relativity. He went on to become a twentieth-century icon-a man whose name and face are synonymous with "genius." Now, at last, ordinary readers can explore Einstein's life and work in this new For Dummies guide. Physicist Carlos Calle chronicles Einstein's career and explains his work-including the theories of special and general relativity-in language that anyone can understand. He shows how Einstein's discoveries affected everything from the development of the atom bomb to the theory of quantum mechanics. He sheds light on Einstein's personal life and beliefs, including his views on religion and politics. And he shows how Einstein's work continues to affect our world today, from nuclear power to space travel to artificial intelligence.




Theory of Orbits


Book Description

Half a century ago, S. Chandrasekhar wrote these words in the preface to his 1 celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ ... ] Indeed, several of the problems of modern stellar dy namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con sidered from the point of view of celestial mechanics (the N-body problem with N» 1), fluid mechanics (the system is represented by a material con tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).




College Physics for AP® Courses


Book Description

"This introductory, algebra-based, two-semester college physics book is grounded with real-world examples, illustrations, and explanations to help students grasp key, fundamental physics concepts. ... This online, fully editable and customizable title includes learning objectives, concept questions, links to labs and simulations, and ample practice opportunities to solve traditional physics application problems."--Website of book.




Discourse on Floating Bodies


Book Description

As to the first, the last discoveries of Saturn to be tricorporeall, and of the mutations of Figure in Venus, like to those that are seen in the Moon, together with the Consequents depending thereupon, have not so much occasioned the demur, as the investigation of the times of the Conversions of each of the Four Medicean Planets about Jupiter, which I lighted upon in April the year past, 1611, at my being in Rome; where, in the end, I assertained my selfe, that the first and neerest to Jupiter, moved about 8 gr. & 29 m. of its Sphere in an houre, makeing its whole revolution in one naturall day, and 18 hours, and almost an halfe. The second moves in its Orbe 14 gr. 13 min. or very neer, in an hour, and its compleat conversion is consummate in 3 dayes, 13 hours, and one third, or thereabouts. The third passeth in an hour, 2 gr. 6 min. little more or less of its Circle, and measures it all in 7 dayes, 4 hours, or very neer. The fourth, and more remote than the rest, goes in one houre, 0 gr 54 min. and almost an halfe of its Sphere, and finisheth it all in 16 dayes, and very neer 18 hours. But because the excessive velocity of their returns or restitutions, requires a most scrupulous precisenesse to calculate their places, in times past and future, especially if the time be for many Moneths or Years; I am therefore forced, with other Observations, and more exact than the former, and in times more remote from one another, to correct the Tables of such Motions, and limit them even to the shortest moment: for such exactnesse my first Observations suffice not; not only in regard of the short intervals of Time, but because I had not as then found out a way to measure the distances between the said Planets by any Instrument: I Observed such Intervals with simple relation to the Diameter of the Body of Jupiter; taken, as we have said, by the eye, the which, though they admit not errors of above a Minute, yet they suffice not for the determination of the exact greatness of the Spheres of those Stars. But now that I have hit upon a way of taking such measures without failing, scarce in a very few Seconds, I will continue the observation to the very occultation of JUPITER, which shall serve to bring us to the perfect knowledge of the Motions, and Magnitudes of the Orbes of the said Planets, together also with some other consequences thence arising. I adde to these things the observation of some obscure Spots, which are discovered in the Solar Body, which changing, position in that, propounds to our consideration a great argument either that the Sun revolves in it selfe, or that perhaps other Starrs, in like manner as Venus and Mercury, revolve about it, invisible in other times, by reason of their small digressions, lesse than that of Mercury, and only visible when they interpose between the Sun and our eye, or else hint the truth of both this and that; the certainty of which things ought not to be contemned, nor omitted.