Newton's Rule Research Articles

Rocket science unveiled: A differential equation exploration of motion

Through the perspective of differential equations, the report "Rocket Science Unveiled" explores the amazing invention of rocket propulsion. In order to study, comprehend, and forecast the behavior of rocket engines, differential equations are essential. In order to better understand and analyze this intricate anomaly, the report aims to investigate the underlying mathematics of rocket propulsion and how differential equations work. We apply the differential equation to clarify the fuel consumption and thrust generation rates. In addition, we utilize Newton's rule of motion to explain the relationship among thrust, mass, and acceleration. Working on this study allowed us to discover the anticipated outcome for both position location and spacecraft position determination. For iterative operations, we used Euler's approach because the analytical calculation of differential equations is complicated, we used Euler's method for iterative operations. Knowing the rocket's initial or previous value allows us to locate or establish its placements with ease.

Free Undamped Motion in Spring Mass System

Assume that a mass m is fastened to the free end of a flexible spring that is hanging vertically from a rigid support [5]. Naturally, the mass of the spring will determine how much it stretches or elongates; different weight masses will stretch the spring in different ways. The spring itself exerts a restoring force F that is proportional to the amount of elongation s and opposed to the direction of elongation, according to Hooke's law. Put simply. When a mass m is connected to a spring, the mass extends the spring by a certain amount, reaching an equilibrium where the restoring force ks balances the mass W. Remember that [6] defines weight. w = mg (0.3.1) the condition of equilibrium is mg = −ks (0.3.2) or mg − ks = 0 (0.3.3) In the event that the mass deviates from its equilibrium position by an amount x, the spring's restoring force is equal to k(x + s). We can associate Newton's second rule with the net, or resultant, force of the restoring force and the weight W is balanced by the restoring force ks, provided that there are no retarding forces operating on the system and that[6] the mass vibrates free of other external forces—free motion. Remember that [6] defines weight. (ⅆ^2 x)/(ⅆt^2 )= -k(s + x) + mg (0.3.5) = −kx + mg − ks = −kx (0.3.5) The spring's restoring force works in the opposite direction of motion, as shown by the negative sign. Additionally, we follow the tradition that displacements recorded in positive values below the equilibrium position [6].

Du Châtelet, induction, and Newton's rules for reasoning

AbstractI examine Du Châtelet's methodology for physics and metaphysics through the lens of her engagement with Newton's Rules for Reasoning in Natural Philosophy. I first show that her early manuscript writings discuss and endorse these Rules. Then, I argue that her famous published account of hypotheses continues to invoke close analogues of Rules 3 and 4, despite various developments in her position. Once relevant experimental evidence and some basic constraints are met, it is legitimate to inductively generalize from observations; general hypotheses can thereafter be assumed as true until contrary experiments show otherwise. I conclude by arguing that this account of induction plays an essential role in her metaphysics, both in an argument for simple substances—which has an inductive premise—and in her attempt to distinguish acceptable and unacceptable metaphysical commitments.

Examination of Rheological Behavior of Water-Based Graphene Oxide Nanofluids

In this study, the rheological properties of nanofluids obtained by loading of Graphene oxide nanoparticles produced by the improved Hummers method into the deionized water base fluid in a mass fraction range of 0.1-1% were investigated. The stability analysis of the nanofluids were conducted through considering the zeta potential measurement values, and all nanofluids were determined as quite stable. Rheological measurements were carried out at 5°C, 15°C, 25°C, and 35°C with using stress-controlled rheometer. Rheological measurements were conducted for two different methods, nonlinear viscoelastic and linear viscoelastic measurements. In nonlinear viscoelastic experiments, the variation of viscosity with the shear rate of the fluid was investigated for both different nanoparticles mass fractions and a fixed constant mass fraction at different temperatures. In the second type of experiments, the elastic behavior of the fluid was determined by measuring frequency-dependent storage G ' and loss modulus G " under small oscillation shear stress. As a result of detailed rheological analysis, it was determined that water based graphene oxide nanofluids containing nanoparticles mass fractions of 0.1% shows a flow behavior that conforms to the Newton’s rule, whereas, due to the increase of graphene oxide mass fractions, the flow behavior changes to the pseudoplastic behavior that does not conform to the Newton's rule. In addition, at high graphene oxide mass fractions, it was seen that the visible viscosity decreased with the increasing temperature. As a result of the conducted linear rheological measurements, it was observed that nanofluids having high concentrated nanoparticle showed viscoelastic behavior properties.

Analysis of Nonlinear Dynamics and Chaos Control in Gear Transmission System with Stochastic Perturbation

In order to study the chaotic characteristics and control chaotic vibration in the gear transmission system. The dynamical equation and the state equation of gear transmission system are established by Newton's rule under considering stochastic perturbation of gear backlash, gear damping ratio, meshing frequency meshing stiffness and input torque fluctuation. The complex dynamics characters of gear transmission system are investigated. Five methods of controlling chaos are used to guide chaotic motions towards regular motions. Numerical simulation shows that the period doubling bifurcation, Hopf bifurcation and chaotic vibration exists in the gear transmission system. The effectiveness and feasibility of two kinds of feedback control method and three kinds of non-feedback control method to get rid of chaos by stabilizing the related unstable periodic orbit are verified.DOI: http://dx.doi.org/10.5755/j01.mech.23.2.13576

Sherlock Holmes and the rules of scientific reasoning [Basic Metrology

Isaac Newton's main work, Philosophiae Naturalis Principia Mathematica, published in 1686, is (as stated in its first American edition) a revolution from the thick darkness of the Middle Ages man's struggling spirit... to the investigation of physical and moral truth. It opened up to the human intellect the stupendous realities of the material world. It is a monument, which glows with the immortality of the transcendent mind ... a true creation of genius, in time and beyond time, forever. In this famous work, Newton not only laid the basis for mechanics and developed the theory of gravitation but also formulated a set of rules of scientific reasoning listed in the sidebar. Rules had also been formulated earlier (and, in fact, can be traced back to Aristotle's), but Newton's rules are stricter and clearer than all previous ones and aim directly at science (instead of theology). His rules replaced the former way of thinking, which was burdened by antiquated prejudices and theological dogma and which lacked clear principles and strength of consequences. Remarkably, Newton's rules have remained valid over the centuries, and our modern scientific world would be unthinkable without them. Nevertheless, this foundation is not generally taught in schools, and not all scientists and engineers are aware of its outstanding importance. Therefore, Newton's rules are listed in the sidebar on the next page and discussed here in a more modern way with some personal comments and examples. Ethical and moral aspects (such as truthful reporting, fair citing, and avoiding rashly sensational reports) are not discussed here and are taken for granted.

Evidence and method: scientific strategies of Isaac Newton and James Clerk Maxwell

Preface Chapter 1: A Problem about Evidence Chapter 2: Newton's Rules Chapter 3: Newtonian Extensions, a Rival, Justifying Induction, and Evidence Chapter 4: What to Do If You Cannot Establish a Theory: Maxwell's Three Methods

Analysis of Bifurcation and Nonlinear Control for Chaos in Gear Transmission System

In order to study the bifurcation characteristics and control chaotic vibration of the gear transmission system. The complex dynamics characters of gear transmission system are studied. The dynamical equation and the state equation of gear transmission system are established according to Newton's rule. The route to chaos of the system is studied by the bifurcation diagram, phase portrait, time course diagram and Poincaré map. A method of controlling chaos by nonlinear feedback controller is developed to guide chaotic motions towards regular motions. Numerical simulation shows that with the increase of meshing stiffness, gear transmission system will be from the periodic motion to chaotic motion by doubling bifurcation, the effectiveness and feasibility of the strategy to get rid of chaos by stabilizing the related unstable periodic orbit.

Dynamics of single rising bubbles in neutrally buoyant liquid-solid suspensions.

We experimentally investigate the effect of particles on the dynamics of a gas bubble rising in a liquid-solid suspension while the particles are equally sized and neutrally buoyant. Using the Stokes number as a universal scale, we show that when a bubble rises through a suspension characterized by a low Stokes number (in our case, small particles), it will hardly collide with the particles and will experience the suspension as a pseudoclear liquid. On the other hand, when the Stokes number is high (large particles), the high particle inertia leads to direct collisions with the bubble. In that case, Newton's collision rule applies, and direct exchange of momentum and energy between the bubble and the particles occurs. We present a simple theory that describes the underlying mechanism determining the terminal bubble velocity.

Kant's Cognitive Semantics, Newton's Rule Four of Philosophy and Scientific Realism

Kant's Critique of Pure Reason contains an original and powerful semantics of singular cognitive reference which has important implications for epistemology and for philosophy of science. Here I argue that Kant's semantics directly and strongly supports Newton's Rule 4 of (natural) Philosophy in ways which support Newton's realism about gravitational force. I begin with Newton's Rule 4 of Philosophy and its role in Newton's justification of realism about gravitational force (§II). Next I briefly summarize Kant's semantics of singular cognitive reference (§III). I then show that the key point of Kant's cognitive semantics is embedded in and strongly supports Newton's Rule 4, and that it rules out not only Cartesian physics (per Harper) but also Cartesian, infallibilist presumptions about empirical justification generally (§IV). Finally, I argue that Kant's semantics reveals a key defect in the original version of Bas van Fraassen's anti-realist ‘Constructive Empiricism’, and in many common objections to realism (§V). Fortunately, Kant's semantics of singular cognitive reference stands independently of his Transcendental Idealism; nothing I argue in this paper depends at all upon that doctrine.In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions. (Newton 1999: 796)

A Class of Complex ICA Algorithms Based on the Kurtosis Cost Function

In this paper, we introduce a novel way of performing real-valued optimization in the complex domain. This framework enables a direct complex optimization technique when the cost function satisfies the Brandwood's independent analyticity condition. In particular, this technique has been used to derive three algorithms, namely, kurtosis maximization using gradient update (KM-G), kurtosis maximization using fixed-point update (KM-F), and kurtosis maximization using Newton update (KM-N), to perform the complex independent component analysis (ICA) based on the maximization of the complex kurtosis cost function. The derivation and related analysis of the three algorithms are performed in the complex domain without using any complex-real mapping for differentiation and optimization. A general complex Newton rule is also derived for developing the KM-N algorithm. The real conjugate gradient algorithm is extended to the complex domain similar to the derivation of complex Newton rule. The simulation results indicate that the fixed-point version (KM-F) and gradient version (KM-G) are superior to other similar algorithms when the sources include both circular and noncircular distributions and the dimension is relatively high.

Double inequalities of Newton's quadrature rule

In this paper double inequalities of Newton's quadrature rule are given.

When physics rules robotics

This article discusses some fundamental issues that arise as robots become much larger or much smaller than everyday human scale. The article's title is respectfully derived from C.J. Pennycuick's Newton Rules Biology: A physical approach to biological problems (1992), from which robot and robotic system designers can learn much from the performance, successes, and failings of biological evolution. Much of the discussion will focus on scaling issues that were first recognized in biological versus technological domains. These issues are discussed mostly from the biological perspective, with the assumption that the reader will have no difficulty extending the underlying principles to technological domains in general, and to the robotics domain specifically. Discussion is also focused on a hypothetical family of geometrically similar vacuum cleaners.

Newton's Rule of Signs for Imaginary Roots

Descartes did not provide a proof for this rule, which forms the basis of the proposition now known as Descartes's Rule of Signs [1],[6]. This rule yields an upper bound for the number of positive (true) roots of a given polynomial and an upper bound for the number of negative (false) roots by counting variations and permanences in the sequence of plus and minus signs obtained from the coefficients of the polynomial

Newton's Rule of Signs for Imaginary Roots

Newton's Rule of Signs for Imaginary Roots

Rough Collisions in Multibody Systems. Restitution Rules and Energetical Consistency

This paper presents a detailed analysis of the energetical inconsistency of the Newton's and Poisson's rules of percussive dynamics when they are applied to rough collisions. The lagrangian formulation of the incremental Routh's model for 3D single point rough collisions in multibody systems is used. For 2D collisions, the energetical inconsistency is analytically formulated, and the energy "creation" associated with these rules is compared to the energy dissipated by friction

Charles Lyell and the Uniformity Principle

The theoretical system Lyell presented in 1830 was composed of three requirements or principles: 1) the Uniformity Principle which states that past geological events must be explained by the same causes now in operation; 2) the Uniformity of Rate Principle which states that geological laws operate with the same force as at present; 3) the Steady-state Principle which states that the earth does not undergo any directional change. The three principles form a single thesis called “uniformitarianism” which has been repeatedly questioned and which has been reputed to be unable to face the competing “directional synthesis” based on the theory of the earth's cooling down. As a result, the significance of Lyell's system has been reduced to a simple “actualism” which admits the validity of the only Uniformity Principle. I believe that the only way to understand Lyell's role in the history of science is to maintain the unity of his synthesis. To show the Newtonian roots of this synthesis I will compare Lyell's principles and Newton's Rules of Reasoning. I will conclude with an analysis of the methodological function of principles in Lyell's scientific endeavour.

Identification of many plane sources in two-dimensional Poisson field

This paper proposes a method for identification of several rectangular uniform plane sources in a two-dimensional Poisson field. When an independent harmonic function is applied to Green's second theorem, as many boundary integral equations as harmonic functions can be obtained. In the case of lumped sources, there are three unknowns: the x and y coordinates of the source location, and the intensity. In the case of a rectangular uniform plane source, there are five unknowns: the x and y coordinates of the center position of the source, the vertical and horizontal lengths of the rectangle, and the intensity. If there are two distributed sources, the problem is reduced to solving 10 nonlinear algebraic equations in 10 unknowns. Eventually, two fourth-order equations containing second and fourth terms and one fourth-order equation containing terms of all orders are solved. By means of the discriminant equation of the quadratic equation for the former and the discriminant equation based on Newton's formula and Descartes' rule of signs, it is determined whether a unique solution can be obtained in the region. When more than three distributed sources exist, it is in principle possible to identify the solutions by this method. However, determination whether a unique solution can be obtained must be studied for each algebraic equation. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(10): 25–32, 1999

The hypothesis of ether and Reid's interpretation of Newton's first rule of philosophizing

My object is to question a recurrent claim made to the point that Thomas Reid (1710–1796) was hostile to ether theories and that this hostility had its source in his distinctive interpretation of the first of Newton's regulae philosophandi. Against this view I will argue that Reid did not have any quarrel at all with unobservable or theoretical entities as such, and that his objections against actual theories concerning ether were scientific rather than philosophical, even when based on Newton's first rule. I argue further that Reid's insistence on Newton's rule concerns, not direct observation, but rather the notion of explanation itself.

The Christian Philosopher by Cotton Mather

100BOOK REVIEWS The Christian Philosopher. By Cotton Mather. Edited with an Introduction and Notes, by Winton U. Solberg. (Urbana and Chicago: University of Illinois Press. 1994. Pp. cxlii, 488. «49.95. ) This splendid edition of Cotton Mather's ambitious natural theology demonstrates one way Puritanism embraced the Enlightenment in Europe. The argument from design, which buttressed natural theology, depended upon empirical observation of natural processes for its assertion that God existed. Like the 'New Science' in Europe, it presumed that like effects proceeded from like causes, Isaac Newton's second rule of reasoning in the Principia. Yet, in its preoccupation with final cause, the argument from design shared more with the Peripatetics than with the experimental philosophers of the seventeenth century. As both Galileo and Bacon warned, teleology too often became tautology. Still, within the swirling cross-currents of the Enlightenment in Britain and eventually in America as well, the logical structures of natural theology often cut across religious boundaries. Orthodox clerics and heterodox pamphleteers often shared fundamental assumptions. Mather's embrace of arguments also invoked by Deists need not compromise his Puritanism. Mather published The Christian Philosopher in 1 72 1 . As Winton Solberg's excellent introduction details, Mather carefully monitored intellectual developments within the Royal Society in London, and often contributed "Curiosa Americana" to their proceedings. He maintained a huge personal library of British books, which he drew upon extensively when compiling his own natural theology. Indeed, as Solberg demonstrates with stunning thoroughness, little of Mather's book proved original. By Solberg's calculations, almost eighty percent of The Christian Philosopher came directly and sometimes without acknowledgment from thepublished works ofsuch figures asJohn Ray, William Derham, John Harris, George Cheyne, and Nehemiah Grew. Mather's personal contribution to this anthology consisted mainly of introductory essays and connective passages which linked his various sources together. Solberg notes forgivingly that such borrowing was widely tolerated in the eighteenth century . He compliments Mather on his extensive knowledge of arcane sources and rightly credits his subject with disseminating the natural theology of the Enlightenment to the American colonies. He also shows how the book influenced both John Wesley and Christian Wolff. Nevertheless, it may come as a surprise to readers just how much Mather lifted from others. Solberg has edited Mather's work with care. His lengthy introduction and extensive notes place the work within its historical context; the handsomely produced text mirrors the original faithfully; the end matter includes a biographical register, a recapitulation of Mather's sources, a list of biblical references , and a useful index. D. L. Le Mahieu Lake Forest College ...