Contribution to mechanics
Newton made an in-depth study on the basis of the work of Galileo and others, and summed up three basic laws of motion of objects (Newton's three laws): ① When any object is not subjected to external force or the resultant force of external force is zero, it keeps its original motion state unchanged, that is, the original motion continues to be static, and the original motion continues to move in a straight line at a constant speed. ② Under the action of external force, the motion state of any object changes, and the rate of change of its momentum with time is directly proportional to the resultant force. Generally speaking, it can be expressed as: the acceleration of an object is directly proportional to the acting force and inversely proportional to the mass of the object, and the direction of acceleration is consistent with the direction of the acting force. (3) When object A gives object B a force, object B must give object A a reaction force at the same time. Force and reaction force are equal in magnitude and opposite in direction, on the same straight line. These three very simple laws of motion have laid a solid foundation for mechanics and exerted great influence on the development of other disciplines. Galileo once put forward the content of the first law, and then R Descartes made a formal improvement, and Galileo also informally mentioned the content of the second law. The content of the third law was obtained by Newton after summing up the achievements of C Lane, J Wallis and C Huygens.
Newton was the discoverer of the law of universal gravitation. He began to think about this problem in 1665 ~ 1666. 1679, R. Hook wrote to him that gravity should be inversely proportional to the square of the distance, and the trajectory of the projectile at the height of the earth is elliptical. Suppose there is a crack in the earth, the projectile will return to its original place, instead of the spiral line towards the center of the earth as Newton imagined. Newton didn't reply, but adopted Hooke's opinion. Based on Kepler's laws of planetary motion and other people's research results, he mathematically deduced the law of universal gravitation.
Newton unified the mechanics of objects on the earth and celestial mechanics into a basic mechanical system and established a classical mechanical theoretical system. It correctly reflects the macro motion law of macro objects at low speed and realizes the first great unity of natural science. This is a leap in human understanding of nature.
Newton pointed out that the viscous resistance of fluid is proportional to the shear rate. He said: the resistance caused by the lack of lubricity between fluid parts, if everything else is the same, is proportional to the separation speed between fluid parts. At present, fluids that conform to this law are called Newtonian fluids, including the most common water and air, and those that do not conform to this law are called non-Newtonian fluids.
When Newton gave the resistance of a flat plate in the airflow, he adopted a particle model for the gas, and concluded that the resistance was proportional to the sine square of the angle of attack. This conclusion is generally incorrect, but because of Newton's authoritative position, later generations have long regarded it as a creed. In the 20th century, T Carmen said humorously when summing up the development of aerodynamics that Newton made the plane go to heaven a century later.
Regarding the speed of sound, Newton correctly pointed out that the speed of sound is directly proportional to the square root of atmospheric pressure and inversely proportional to the square root of density. However, because he regards sound propagation as an isothermal process, the result is inconsistent with reality. Later, P.-S. Laplace revised Newton's formula of sound speed from the perspective of adiabatic process.
Contribution to mathematics
Since17th century, the original geometry and algebra have been difficult to solve many new problems raised by production and natural science at that time, such as: how to find the instantaneous velocity and acceleration of an object? How to find the tangent of the curve and the length of the curve (planetary distance), the area swept by the vector diameter, the minimum value (such as perihelion, apohelion, maximum range, etc.). ), volume, center of gravity, gravity, etc.; Although Newton had made some achievements in logarithm, analytic geometry and infinite series before, he could not solve these problems satisfactorily or universally. The greatest influences on Newton at that time were Descartes' Geometry and Varis's arithmetica infinitorum. Newton unified various special methods for solving infinitesimal problems since ancient Greece into two algorithms: downstream calculus (differential) and countercurrent calculus (integral), which are embodied in the application of infinite polynomial equation in 1669, stream calculus and infinite series in 167 1 and infinite series in 1676. The so-called "flow" is an independent variable that changes with time, such as x, y, s, u, etc. The "flow number" is the speed of flow change, that is, the rate of change, writing, etc. There is a difference between the "differential rate" and the "variable rate" he said. At the same time, he first published his binomial expansion theorem in 1676. Newton used it to discover other infinite series, and used it to calculate areas, integrals, solve equations and so on. 1684, Leibniz introduced and lengthened S as the symbol of calculus from the tangent study of curves, and the calculus founded by Newton was rapidly popularized in mainland countries.
The appearance of calculus has become another important branch in the development of mathematics besides geometry and algebra-mathematical analysis (Newton called it "analysis by the method of infinite polynomial equation"), and further developed into differential geometry, differential equation, variational method and so on, thus promoting the development of theoretical physics. For example, J Bernoulli of Switzerland seeks the solution of the steepest descent curve, which is the initial problem of variational method, and no mathematician in Europe can answer it within half a year. 1697, Newton overheard it one day, and it was solved in one fell swoop that night, and it was published anonymously in the Journal of Philosophy. Bernoulli said in surprise, "I recognized the lion from this claw."
Newton put forward the "flow method" on the basis of predecessors' work, established binomial theorem, and founded calculus almost at the same time with G.W. Leibniz, and obtained the concepts and operation rules of derivative and integral, clarifying that derivative and integral are reciprocal operations, which opened up a new era for the development of mathematics.