Mechanics in the context of Impact force

Pappus of Alexandria (/ˈpæpəs/ ; Ancient Greek: Πάππος ὁ Ἀλεξανδρεύς; c. 290 – c.  350 AD) was a Greek mathematician of late antiquity known for his Synagoge (Συναγωγή) or Collection (c. 340), and for Pappus's hexagon theorem in projective geometry. Almost nothing is known about his life except for what can be found in his own writings, many of which are lost. Pappus apparently lived in Alexandria, where he worked as a mathematics teacher to higher level students, one of whom was named Hermodorus.

The Collection, his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics that were part of the ancient mathematics curriculum, including geometry, astronomy, and mechanics.

Christiaan Huygens, Lord of Zeelhem, FRS (/ˈhaɪɡənz/ HY-gənz, US also /ˈhɔɪɡənz/ HOY-gənz; Dutch: [ˈkrɪstijaːn ˈɦœyɣə(n)s] ; also spelled Huyghens; Latin: Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution. In physics, Huygens made seminal contributions to optics and mechanics, while as an astronomer he studied the rings of Saturn and discovered its largest moon, Titan. As an engineer and inventor, he improved the design of telescopes and invented the pendulum clock, the most accurate timekeeper for almost 300 years. A talented mathematician and physicist, his works contain the first idealization of a physical problem by a set of mathematical parameters, and the first mathematical and mechanistic explanation of an unobservable physical phenomenon.

Huygens first identified the correct laws of elastic collision in his work De Motu Corporum ex Percussione, completed in 1656 but published posthumously in 1703. In 1659, Huygens derived geometrically the formula in classical mechanics for the centrifugal force in his work De vi Centrifuga, a decade before Isaac Newton. In optics, he is best known for his wave theory of light, which he described in his Traité de la Lumière (1690). His theory of light was initially rejected in favour of Newton's corpuscular theory of light, until Augustin-Jean Fresnel adapted Huygens's principle to give a complete explanation of the rectilinear propagation and diffraction effects of light in 1821. Today this principle is known as the Huygens–Fresnel principle.

China has been the source of many innovations, scientific discoveries and inventions. This includes the Four Great Inventions: papermaking, the compass, gunpowder, and early printing (both woodblock and movable type). The list below contains these and other inventions in ancient and modern China attested by archaeological or historical evidence, including prehistoric inventions of Neolithic and early Bronze Age China.

The historical region now known as China experienced a history involving mechanics, hydraulics and mathematics applied to horology, metallurgy, astronomy, agriculture, engineering, music theory, craftsmanship, naval architecture and warfare. Use of the plow during the Neolithic period Longshan culture (c. 3000 – c. 2000 BC) allowed for high agricultural production yields and rise of Chinese civilization during the Shang dynasty (c. 1600 – c. 1050 BC). Later inventions such as the multiple-tube seed drill and the heavy moldboard iron plow enabled China to sustain a much larger population through improvements in agricultural output.

William Whewell (/ˈhjuːəl/ HEW-əl; 24 May 1794 – 6 March 1866) was an English polymath. He was Master of Trinity College, Cambridge. In his time as a student there, he achieved distinction in both poetry and mathematics.

The breadth of Whewell's endeavours is his most remarkable feature. In a time of increasing specialisation, Whewell belonged in an earlier era when natural philosophers investigated widely. He published work in mechanics, physics, geology, astronomy, and economics, while also composing poetry, writing a Bridgewater Treatise, translating the works of Goethe, and writing sermons and theological tracts. In mathematics, Whewell introduced what is now called the Whewell equation, defining the shape of a curve without reference to an arbitrarily chosen coordinate system. He also organized thousands of volunteers internationally to study ocean tides, in what is now considered one of the first citizen science projects. He received the Royal Medal for this work in 1837.

In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. For a rigid body containing its center of mass, this is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for the application of Newton's laws of motion.

In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a distribution of separate bodies, such as the planets of the Solar System, the center of mass may not correspond to the position of any individual member of the system.

Jean-Baptiste le Rond d'Alembert (/ˌdæləmˈbɛər/ DAL-əm-BAIR; French: [ʒɑ̃ batist lə ʁɔ̃ dalɑ̃bɛʁ]; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the Encyclopédie. D'Alembert's formula for obtaining solutions to the wave equation is named after him. The wave equation is sometimes referred to as d'Alembert's equation, and the fundamental theorem of algebra is named after d'Alembert in French.

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space. Its length represents the distance in relation to an arbitrary reference origin O, and its direction represents the angular orientation with respect to given reference axes. Usually denoted x, r, or s, it corresponds to the straight line segment from O to P.In other words, it is the displacement or translation that maps the origin to P:

The term position vector is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.Frequently this is used in two-dimensional or three-dimensional space, but can be easily generalized to Euclidean spaces and affine spaces of any dimension.

In mechanics, vibration (from Latin vibrāre 'to shake') is oscillatory motion about an equilibrium point. Vibration may be deterministic if the oscillations can be characterised precisely (e.g. the periodic motion of a pendulum), or random if the oscillations can only be analysed statistically (e.g. the movement of a tire on a gravel road).

Vibration can be desirable: for example, the motion of a tuning fork, the reed in a woodwind instrument or harmonica, a mobile phone, or the cone of a loudspeaker.In many cases, however, vibration is undesirable, wasting energy and creating unwanted sound. For example, the vibrational motions of engines, electric motors, or any mechanical device in operation are typically unwanted. Such vibrations could be caused by imbalances in the rotating parts, uneven friction, or the meshing of gear teeth. Careful designs usually minimize unwanted vibrations.

An analog computer or analogue computer is a type of computation machine (computer) that uses physical phenomena such as electrical, mechanical, or hydraulic quantities behaving according to the mathematical principles in question (analog signals) to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude (digital signals).

Analog computers can have a very wide range of complexity. Slide rules and nomograms are the simplest, while naval gunfire control computers and large hybrid digital/analog computers were among the most complicated. Complex mechanisms for process control and protective relays used analog computation to perform control and protective functions. The common property of all of them is that they don't use algorithms to determine the fashion of how the computer works. They rather use a structure analogous to the system to be solved (a so called analogon, model or analogy) which is also eponymous to the term analog computer, because they represent a model.

Principles of Philosophy (Latin: Principia Philosophiae) is a book by the French philosopher and scientist René Descartes. In essence, it is a synthesis of the Discourse on Method and Meditations on First Philosophy. It was written in Latin, published in 1644 and dedicated to Elisabeth of Bohemia, with whom Descartes had a long-standing friendship. A French version (Les Principes de la Philosophie) followed in 1647.

The book sets forth the principles of nature—the laws of physics—as Descartes viewed them. Most notably, it set forth the principle that in the absence of external forces, an object's motion will be uniform and in a straight line. Isaac Newton borrowed this principle from Descartes and included it in his own Principia; to this day, it is still generally referred to as Newton's first law of motion. The book was primarily intended to replace the Aristotelian curriculum then used in French and British universities. The work provides a systematic statement of his metaphysics and natural philosophy, and represents the first truly comprehensive, mechanistic account of the universe.

In physics and mechanics, torque is the rotational correspondent of linear force. It is also referred to as the moment of force, or simply the moment. The symbol for torque is typically ${\displaystyle {\boldsymbol {\tau }}}$, the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M. Just as a linear force is a push or a pull applied to a body, a torque can be thought of as a twist applied to an object with respect to a chosen point; for example, driving a screw uses torque to force it into an object, which is applied by the screwdriver rotating around its axis to the drives on the head.

Torque is generally referred to using different vocabulary depending on geographical location and field of study, with torque generally being associated with physics and moment being associated with engineering. This article follows the definition used in US physics in its usage of the word torque.

Mechanical engineering is the study of physical machines and mechanisms that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, and maintain mechanical systems. It is one of the oldest and broadest of the engineering branches.

Mechanical engineering requires an understanding of core areas including mechanics, dynamics, thermodynamics, materials science, design, structural analysis, and electricity. In addition to these core principles, mechanical engineers use tools such as computer-aided design (CAD), computer-aided manufacturing (CAM), computer-aided engineering (CAE), and product lifecycle management to design and analyze manufacturing plants, industrial equipment and machinery, heating and cooling systems, transport systems, motor vehicles, aircraft, watercraft, robotics, medical devices, weapons, and others.

A lock is a mechanical or electronic fastening device that is released by a physical object (such as a key, keycard, fingerprint, RFID card, security token or coin), by supplying secret information (such as a number or letter permutation or password), by a combination thereof, or it may only be able to be opened from one side, such as a door chain.

A key is a device that is used to operate a lock (to lock or unlock it). A typical key is a small piece of metal consisting of two parts: the bit or blade, which slides into the keyway of the lock and distinguishes between different keys, and the bow, which is left protruding so that torque can be applied by the user. In its simplest implementation, a key operates one lock or set of locks that are keyed alike, a lock/key system where each similarly keyed lock requires the same, unique key.

In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation that maps the initial position to the final position. Displacement is the shift in location when an object in motion changes from one position to another.For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude is the average speed (a scalar quantity).

In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the orientation of the net force acting on that object. The magnitude of an object's acceleration, as described by Newton's second law, is the combined effect of two causes:

• the net balance of all external forces acting onto that object — magnitude is directly proportional to this net resulting force;
• that object's mass, depending on the materials out of which it is made — magnitude is inversely proportional to the object's mass.

The SI unit for acceleration is metre per second squared (m⋅s, ${\displaystyle \mathrm {\tfrac {m}{s^{2}}} }$).

In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non-quantum mechanical description of a system of particles, or of a fluid, in cases where the velocities of moving objects are comparable to the speed of light c. As a result, classical mechanics is extended correctly to particles traveling at high velocities and energies, and provides a consistent inclusion of electromagnetism with the mechanics of particles. This was not possible in Galilean relativity, where it would be permitted for particles and light to travel at any speed, including faster than light. The foundations of relativistic mechanics are the postulates of special relativity and general relativity. The unification of SR with quantum mechanics is relativistic quantum mechanics, while attempts for that of GR is quantum gravity, an unsolved problem in physics.

As with classical mechanics, the subject can be divided into "kinematics"; the description of motion by specifying positions, velocities and accelerations, and "dynamics"; a full description by considering energies, momenta, and angular momenta and their conservation laws, and forces acting on particles or exerted by particles. There is however a subtlety; what appears to be "moving" and what is "at rest"—which is termed by "statics" in classical mechanics—depends on the relative motion of observers who measure in frames of reference.

The natural sciences saw various advancements during the Golden Age of Islam (from roughly the mid 8th to the mid 13th centuries), adding a number of innovations to the Transmission of the Classics (such as Aristotle, Ptolemy, Euclid, Neoplatonism). During this period, Islamic theology was encouraging of thinkers to find knowledge. Thinkers from this period included Al-Farabi, Abu Bishr Matta, Ibn Sina, al-Hassan Ibn al-Haytham and Ibn Bajjah. These works and the important commentaries on them were the wellspring of science during the medieval period. They were translated into Arabic, the lingua franca of this period.

Islamic scholarship in the sciences had inherited Aristotelian physics from the Greeks and during the Islamic Golden Age developed it further. However the Islamic world had a greater respect for knowledge gained from empirical observation, and believed that the universe is governed by a single set of laws. Their use of empirical observation led to the formation of crude forms of the scientific method. The study of physics in the Islamic world started in Iraq and Egypt. Fields of physics studied in this period include optics, mechanics (including statics, dynamics, kinematics and motion), and astronomy.

The Mathematical Sciences are a group of areas of study that includes, in addition to mathematics, those academic disciplines that are primarily mathematical in nature but may not be universally considered subfields of mathematics proper.

Statistics, for example, is mathematical in its methods but grew out of bureaucratic and scientific observations, which merged with inverse probability and then grew through applications in some areas of physics, biometrics, and the social sciences to become its own separate, though closely allied, field. Theoretical astronomy, theoretical physics, theoretical and applied mechanics, continuum mechanics, mathematical chemistry, actuarial science, computer science, computational science, data science, operations research, quantitative biology, control theory, econometrics, geophysics and mathematical geosciences are likewise other fields often considered part of the mathematical sciences.