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Glossary of aerospace engineering

From Wikipedia, the free encyclopedia
List of definitions of terms and concepts commonly used in aerospace engineering

This glossary ofaerospace engineering terms pertains specifically toaerospace engineering, its sub-disciplines, and related fields includingaviation andaeronautics. For a broad overview of engineering, seeglossary of engineering.

A

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B

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This stabilizes the ballute as it decelerates through different flow regimes (from supersonic to subsonic).

  • Beam-powered propulsion – also known as directed energy propulsion, is a class ofaircraft orspacecraft propulsion that uses energy beamed to the spacecraft from a remote power plant to provide energy. The beam is typically either amicrowave or alaser beam and it is either pulsed or continuous. A continuous beam lends itself tothermal rockets, photonic thrusters andlight sails, whereas a pulsed beam lends itself to ablative thrusters andpulse detonation engines.[28]
  • Bearing – Innavigation, bearing is the horizontal angle between the direction of an object and another object, or between it and that of true north.Absolute bearing refers to the angle between the magnetic North (magnetic bearing) or true North (true bearing) and an object. For example, an object to the East would have an absolute bearing of 90 degrees.Relative bearing refers to the angle between the craft's forward direction, and the location of another object. For example, an object relative bearing of 0 degrees would be dead ahead; an object relative bearing 180 degrees would be behind.[29] Bearings can be measured inmils or degrees.
  • Bernoulli's principle – Influid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease inpressure or a decrease in thefluid'spotential energy.[30]: Ch.3 [31]: 156–164, § 3.5 
  • Bi-elliptic transfer – is anorbital maneuver that moves aspacecraft from oneorbit to another and may, in certain situations, require lessdelta-v than aHohmann transfer maneuver. The bi-elliptic transfer consists of two half-elliptic orbits. From the initial orbit, a first burn expends delta-v to boost the spacecraft into the first transfer orbit with anapoapsis at some pointrb{\displaystyle r_{b}} away from thecentral body. At this point a second burn sends the spacecraft into the second elliptical orbit withperiapsis at the radius of the final desired orbit, where a third burn is performed, injecting the spacecraft into the desired orbit.[32]
  • Big dumb booster – (BDB), is a general class oflaunch vehicle based on the premise that it is cheaper to operate large rockets of simple design than it is to operate smaller, more complex ones regardless of the lower payload efficiency.[33]
  • Bleed air – produced bygas turbine engines iscompressed air that is taken from the compressor stage of those engines, which is upstream of the fuel-burning sections.
  • Booster – A boosterrocket (or engine) is either the first stage of amultistagelaunch vehicle, or else a shorter-burning rocket used in parallel with longer-burningsustainer rockets to augment thespace vehicle's takeoff thrust and payload capability.[34][35]
  • Boundary layer – Inphysics andfluid mechanics, a boundary layer is an important concept and refers to the layer offluid in the immediate vicinity of abounding surface where the effects of viscosity are significant. In theEarth's atmosphere, theatmospheric boundary layer is the air layer near the ground affected by diurnal heat, moisture or momentum transfer to or from the surface. On anaircraftwing the boundary layer is the part of the flow close to the wing, whereviscousforces distort the surrounding non-viscous flow.
  • Buoyancy – Inphysics, buoyancy orupthrust, is an upwardforce exerted by afluid that opposes theweight of an immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. This pressure difference results in a net upwards force on the object. The magnitude of that force exerted is proportional to that pressure difference, and (as explained byArchimedes' principle) is equivalent to the weight of the fluid that would otherwise occupy the volume of the object, i.e. thedisplaced fluid.

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  • Cabin pressurization – is a process in which conditioned air is pumped into thecabin of an aircraft orspacecraft, in order to create a safe and comfortable environment for passengers and crew flying at high altitudes. For aircraft, this air is usuallybled off from thegas turbine engines at the compressor stage, and for spacecraft, it is carried in high-pressure, oftencryogenic tanks. The air is cooled, humidified, and mixed with recirculated air if necessary, before it is distributed to the cabin by one or moreenvironmental control systems.[36] The cabin pressure is regulated by the outflow valve.
  • Cable lacing – is a method for tyingwiring harnesses and cable looms, traditionally used intelecommunication, naval, and aerospace applications. This oldcable management technique, taught to generations oflinemen,[37] is still used in some modern applications since it does not create obstructions along the length of the cable, avoiding the handling problems of cables groomed by plastic orhook-and-loopcable ties.
  • Camber – the asymmetric curves on the top and bottom, or front and back, of an aerofoil
  • Canard – is anaeronautical arrangement wherein a small forewing or foreplane is placed forward of the main wing of afixed-wing aircraft. The term "canard" may be used to describe the aircraft itself, thewing configuration or the foreplane.[38][39][40]
  • Centennial challenges
  • Center of gravity – A body's center of gravity is the point around which theresultant torque due to gravity forces vanishes. Where a gravity field can be considered to be uniform, the mass-center and the center-of-gravity will be the same. However, for satellites in orbit around a planet, in the absence of other torques being applied to a satellite, the slight variation (gradient) in gravitational field between closer-to (stronger) and further-from (weaker) the planet can lead to a torque that will tend to align the satellite such that its long axis is vertical. In such a case, it is important to make the distinction between the center-of-gravity and the mass-center. Any horizontal offset between the two will result in an applied torque.
  • Center of mass – Inphysics, thecenter of mass of a distribution ofmass in space is the unique point where theweighted relativeposition of the distributed mass sums to zero, or the point where if a force is applied it moves in the direction of the force without rotating. The distribution of mass is balanced around the center of mass and the average of the weighted position coordinates of the distributed mass defines its coordinates.
  • Center of pressure – is the point where the total sum of apressure field acts on a body, causing aforce to act through that point.
  • Centrifugal compressorCentrifugal compressors, sometimes calledradial compressors, are a sub-class of dynamic axisymmetric work-absorbingturbomachinery.[41] They achieve a pressure rise by addingkinetic energy/velocity to a continuous flow offluid through the rotor orimpeller. This kinetic energy is then converted to an increase inpotential energy/static pressure by slowing theflow through a diffuser. The pressure rise in the impeller is in most cases almost equal to the rise in the diffuser.
  • Chord – is the imaginary straight line joining the leading and trailing edges of anaerofoil. Thechord length is the distance between thetrailing edge and the point on the leading edge where the chord intersects theleading edge.[42][43]
  • Clean configuration – is the flight configuration of afixed-wing aircraft when its external equipment is retracted to minimize drag and thus maximizeairspeed for a given power setting.
  • Cockpit – orflight deck, is the area, usually near the front of anaircraft orspacecraft, from which apilot controls the aircraft.
  • Collimated beam – Acollimated beam oflight or otherelectromagnetic radiation has parallelrays, and therefore will spread minimally as it propagates. A perfectly collimatedlight beam, with nodivergence, would not disperse with distance. Such a beam cannot be created, due todiffraction.[44]
  • Comet – is an icy,small Solar System body that, when passing close to theSun, warms and begins to release gases, a process calledoutgassing. This produces a visible atmosphere orcoma, and sometimes also atail.
  • Compressibility – Inthermodynamics andfluid mechanics,compressibility (also known as the coefficient of compressibility[45] or isothermal compressibility[46]) is ameasure of the relative volume change of afluid orsolid as a response to apressure (or meanstress) change. In its simple form, the compressibilityβ{\displaystyle \beta } may be expressed as
β=1VVp{\displaystyle \beta =-{\frac {1}{V}}{\frac {\partial V}{\partial p}}}, whereV isvolume andp is pressure. The choice to define compressibility as theopposite of the fraction makes compressibility positive in the (usual) case that an increase in pressure induces a reduction in volume. t is also known as reciprocal of bulk modulus(k) of elasticity of a fluid.
  • Compression – Inmechanics,compression is the application of balanced inward ("pushing") forces to different points on a material or structure, that is, forces with no net sum ortorque directed so as to reduce its size in one or more directions.[47] It is contrasted withtension or traction, the application of balanced outward ("pulling") forces; and withshearing forces, directed so as to displace layers of the material parallel to each other. Thecompressive strength of materials and structures is an important engineering consideration.
  • Compressor map – is a diagram showing significant performance parameters for a rotating compressor, and how they vary with changing ambient conditions of pressure and temperature.
  • Computational fluid dynamics – (CFD), is a branch offluid mechanics that usesnumerical analysis anddata structures to analyze and solve problems that involvefluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids andgases) with surfaces defined byboundary conditions. With high-speedsupercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems.
  • Conservation of momentum – The total momentum of objects involved in a collision remains constant regardless of friction and permanent deformation that may occur during the collision. The law of conservation of momentum can be used to analyse the interactions between objects, even in the presence of friction and other non-conservative forces. Conservation of momentum is a consequence of Newton's laws of motion.
  • Constant speed drive – (CSD), is a type oftransmission that takes an input shaft rotating at a wide range of speeds, delivering this power to an output shaft that rotates at a constant speed, despite the varying input. They are used to drive mechanisms, typicallyelectrical generators, that require a constant input speed. The term is most commonly applied tohydraulic transmissions found on theaccessory drives ofgas turbine engines, such as aircraftjet engines. On modern aircraft, the CSD is often combined with a generator into a single unit known as anintegrated drive generator (IDG).
  • Control engineering – orcontrol systems engineering, is anengineering discipline that appliesautomatic control theory to design systems with desired behaviors incontrol environments.[48] The discipline of controls overlaps and is usually taught along withelectrical engineering at many institutions around the world.[48]
  • Controllability
  • Crew Exploration Vehicle
  • Critical mach – Inaerodynamics, thecritical Mach number (Mcr or M* ) of anaircraft is the lowestMach number at which the airflow over some point of the aircraft reaches thespeed of sound, but does not exceed it.[49] At thelower critical Mach number, airflow around the entire aircraft is subsonic. At theupper critical Mach number, airflow around the entire aircraft is supersonic.[50]
  • Cylinder stress – Inmechanics, acylinder stress is astress distribution withrotational symmetry; that is, which remains unchanged if the stressed object is rotated about some fixed axis.

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  • Damage tolerance – is a property of a structure relating to its ability to sustain defects safely until repair can be effected. The approach to engineering design to account for damage tolerance is based on the assumption that flaws can exist in any structure and such flaws propagate with usage.
  • Decalage – Decalage on afixed-wing aircraft is the angle difference between the upper and lower wings of abiplane, i.e. the acute angle contained between thechords of the wings in question. Decalage is said to be positive when the upper wing has a higherangle of incidence than the lower wing, and negative when the lower wing's incidence is greater than that of the upper wing. Positive decalage results in greater lift from the upper wing than the lower wing, the difference increasing with the amount of decalage.[51]
  • De Laval nozzle – (orconvergent-divergent nozzle,CD nozzle orcon-di nozzle), is a tube that is pinched in the middle, making a carefully balanced, asymmetrichourglass shape. It is used to accelerate a hot, pressurizedgas passing through it to a highersupersonic speed in the axial (thrust) direction, by converting the heat energy of the flow intokinetic energy. Because of this, thenozzle is widely used in some types ofsteam turbines androcket engine nozzles. It also sees use in supersonicjet engines.
  • Dead reckoning – Innavigation, dead reckoning is the process of calculating one's current position by using a previously determined position, orfix, and advancing that position based upon known or estimated speeds over elapsed time and course.
  • Deflection – is the degree to which a structural element is displaced under aload. It may refer to an angle or a distance.
  • Deformation (engineering) – Inmaterials science, deformation refers to any changes in the shape or size of an object due to an appliedforce (the deformation energy, in this case, is transferred through work) or a change in temperature (the deformation energy, in this case, is transferred through heat).
  • Deformation (mechanics) – incontinuum mechanics is the transformation of a body from areference configuration to acurrent configuration.[52] A configuration is a set containing the positions of all particles of the body. A deformation may be caused byexternal loads,[53]body forces (such asgravity orelectromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc.
  • Delta-v – (literally "change invelocity"), symbolised asv and pronounceddelta-vee, as used inspacecraft flight dynamics, is a measure of theimpulse that is needed to perform a maneuver such as launch from, or landing on a planet or moon, or in-spaceorbital maneuver. It is ascalar that has the units ofspeed. As used in this context, it isnot the same as thephysical change in velocity of the vehicle.
  • Delta-v budget – is an estimate of the totaldelta-v required for aspace mission. It is calculated as the sum of the delta-v required for thepropulsivemaneuvers during the mission, and as input to theTsiolkovsky rocket equation, determines how much propellant is required for a vehicle of given mass and propulsion system.
  • Delta wing – is awing shaped in the form of a triangle. It is named for its similarity in shape to the Greek uppercase letterdelta (Δ). Although long studied, it did not find significant applications until thejet age, when it proved suitable for high-speed subsonic and supersonic flight.
  • Density
  • Departure resistance – is a quality of anaircraft which enables it to remain in controlled flight and resist entering potentially dangerous less-controlled maneuvers such asspin.
  • Derivative – The derivative of afunction of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool ofcalculus. For example, the derivative of the position of a moving object with respect totime is the object'svelocity: this measures how quickly the position of the object changes when time advances.
  • Digital Datcom – TheUnited StatesAir Force Stability and Control Digital DATCOM is a computer program that implements the methods contained in theUSAF Stability and Control DATCOM to calculate the static stability, control and dynamic derivative characteristics offixed-wing aircraft. Digital DATCOM requires an input file containing a geometric description of an aircraft, and outputs its corresponding dimensionless stability derivatives according to the specified flight conditions. The values obtained can be used to calculate meaningful aspects offlight dynamics.
  • Dihedral – Dihedral angle is the upward angle from horizontal of the wings or tailplane of afixed-wing aircraft. "Anhedral angle" is the name given to negative dihedral angle, that is, when there is adownward angle from horizontal of the wings or tailplane of a fixed-wing aircraft.
  • Disk loading – Influid dynamics, disk loading or disc loading is the averagepressure change across anactuator disk, such as an airscrew. Airscrews with a relatively low disk loading are typically called rotors, includinghelicoptermain rotors andtail rotors;propellers typically have a higher disk loading.[54]
  • Displacement (vector)
  • Distance measuring equipment – (DME), is a radio navigation technology that measures theslant range (distance) between an aircraft and a ground station by timing thepropagation delay of radio signals in the frequency band between 960 and 1215 megahertz (MHz). Line-of-visibility between the aircraft and ground station is required. An interrogator (airborne) initiates an exchange by transmitting a pulse pair, on an assigned 'channel', to the transponder ground station. The channel assignment specifies the carrier frequency and the spacing between the pulses. After a known delay, the transponder replies by transmitting a pulse pair on a frequency that is offset from the interrogation frequency by 63 MHz and having specified separation.[55]
  • DME – distance measuring equipment.
  • DO-178B
  • DO-254
  • Drag (physics) – Influid dynamics, drag (sometimes called air resistance, a type offriction, or fluid resistance, another type of friction or fluid friction) is aforce acting opposite to the relative motion of any object moving with respect to a surrounding fluid.[56] This can exist between two fluid layers (or surfaces) or a fluid and asolid surface. Unlike other resistive forces, such as dryfriction, which are nearly independent of velocity, drag forces depend on velocity.[57][58] Drag force is proportional to the velocity for alaminar flow and the squared velocity for aturbulent flow. Even though the ultimate cause of a drag is viscous friction, the turbulent drag is independent ofviscosity.[59] Drag forces always decrease fluid velocity relative to the solid object in the fluid'spath.
  • Drag coefficient – Influid dynamics, the drag coefficient (commonly denoted as:Cd{\displaystyle \scriptstyle C_{\mathrm {d} }\,},Cx{\displaystyle \scriptstyle C_{\mathrm {x} }\,} orCw{\displaystyle \scriptstyle C_{\mathrm {w} }\,}) is adimensionless quantity that is used to quantify thedrag or resistance of an object in a fluid environment, such as air or water. It is used in thedrag equation in which a lower drag coefficient indicates the object will have lessaerodynamic orhydrodynamic drag. The drag coefficient is always associated with a particular surface area.[60]
  • Drag equation – Influid dynamics, the drag equation is a formula used to calculate the force ofdrag experienced by an object due to movement through a fully enclosingfluid. The equation is:
FD=12ρu2CDA{\displaystyle F_{D}\,=\,{\tfrac {1}{2}}\,\rho \,u^{2}\,C_{D}\,A}
FD{\displaystyle F_{D}} is the dragforce, which is by definition the force component in the direction of the flow velocity,
ρ{\displaystyle \rho } is themass density of the fluid,[61]
u{\displaystyle u} is theflow velocity relative to the object,
A{\displaystyle A} is the referencearea, and
CD{\displaystyle C_{D}} is thedrag coefficient – adimensionlesscoefficient related to the object's geometry and taking into account bothskin friction andform drag. In general,CD{\displaystyle C_{D}} depends on theReynolds number.

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Given a domainΩRn{\displaystyle \Omega \subseteq \mathbb {R} ^{n}} and a once-weakly differentiable vector fielduH1(Rn)n{\displaystyle u\in H^{1}(\mathbb {R} ^{n})^{n}} which represents a fluid flow, such as a solution to theNavier-Stokes equations, its enstrophy is given by:[67]
E(u):=Ω|u|2dx{\displaystyle {\mathcal {E}}(u):=\int _{\Omega }|\nabla \mathbf {u} |^{2}\,dx}
Where|u|2=i,j=1n|iuj|2{\displaystyle |\nabla \mathbf {u} |^{2}=\sum _{i,j=1}^{n}\left|\partial _{i}u^{j}\right|^{2}}. This is quantity is the same as the squaredseminorm|u|H1(Ω)n2{\displaystyle |\mathbf {u} |_{H^{1}(\Omega )^{n}}^{2}}of the solution in theSobolev space ::::H1(Ω)n{\displaystyle H^{1}(\Omega )^{n}}.
In the case that the flow isincompressible, or equivalently thatu=0{\displaystyle \nabla \cdot \mathbf {u} =0}, the enstrophy can be described as the integral of the square of thevorticityω{\displaystyle \mathbf {\omega } },[68]
E(ω)Ω|ω|2dx{\displaystyle {\mathcal {E}}({\boldsymbol {\omega }})\equiv \int _{\Omega }|{\boldsymbol {\omega }}|^{2}\,dx}
or, in terms of theflow velocity,
E(u)S|×u|2dS.{\displaystyle {\mathcal {E}}(\mathbf {u} )\equiv \int _{S}|\nabla \times \mathbf {u} |^{2}\,dS\,.}
In the context of the incompressible Navier-Stokes equations, enstrophy appears in the following useful result[20]
ddt(12Ω|u|2)=νE(u){\displaystyle {\frac {d}{dt}}\left({\frac {1}{2}}\int _{\Omega }|\mathbf {u} |^{2}\right)=-\nu {\mathcal {E}}(\mathbf {u} )}
The quantity in parentheses on the left is the energy in the flow, so the result says that energy declines proportional to thekinematic viscosityν{\displaystyle \nu } times the enstrophy.

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2ut2=c22ux2{\displaystyle {\frac {\partial ^{2}u}{\partial t^{2}}}=c^{2}{\frac {\partial ^{2}u}{\partial x^{2}}}}
The equation has the property that, ifu and its first time derivative are arbitrarily specified initial data on the linet = 0 (with sufficient smoothness properties), then there exists a solution for all timet.
  • Hypersonic speed – Inaerodynamics, a hypersonic speed is one that greatly exceeds thespeed of sound, often stated as starting at speeds ofMach 5 and above.[99] The preciseMach number at which a craft can be said to be flying at hypersonic speed varies, since individual physical changes in the airflow (like moleculardissociation andionization) occur at different speeds; these effects collectively become important around Mach 5–10. The hypersonic regime can also be alternatively defined as speeds where specific heat capacity changes with the temperature of the flow as kinetic energy of the moving object is converted into heat.[100]
  • Hypoxia – is a condition[101] in which the body or a region of the body is deprived of adequateoxygen supply at thetissue level. Hypoxia may be classified as eithergeneralized, affecting the whole body, orlocal, affecting a region of the body.[102] Although hypoxia is often apathological condition, variations in arterial oxygen concentrations can be part of the normal physiology, for example, duringhypoventilation training or strenuous physical exercise.

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  1. The orbit of a planet is anellipse with the Sun at one of the two foci.
  2. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
  3. The square of a planet'sorbital period is proportional to the cube of the length of thesemi-major axis of its orbit.
The elliptical orbits of planets were indicated by calculations of the orbit ofMars. From this, Kepler inferred that other bodies in theSolar System, including those farther away from the Sun, also have elliptical orbits. The second law helps to establish that when a planet is closer to the Sun, it travels faster. The third law expresses that the farther a planet is from the Sun, the slower its orbital speed, and vice versa.
Isaac Newton showed in 1687 that relationships like Kepler's would apply in the Solar System as a consequence of his ownlaws of motion andlaw of universal gravitation.
Kuethe and Schetzer state the Kutta condition as follows:[121]: § 4.11 
A body with a sharp trailing edge which is moving through a fluid will create about itself acirculation of sufficient strength to hold the rearstagnation point at the trailing edge.
In fluid flow around a body with a sharp corner, the Kutta condition refers to the flow pattern in which fluid approaches the corner from above and below, meets at the corner, and then flows away from the body. None of the fluid flows around the sharp corner.
The Kutta condition is significant when using theKutta–Joukowski theorem to calculate the lift created by an airfoil with a sharp trailing edge. The value ofcirculation of the flow around the airfoil must be that value that would cause the Kutta condition to exist.
  • Kutta–Joukowski theorem – is a fundamental theorem inaerodynamics used for the calculation of lift of anairfoil and any two-dimensional bodies including circular cylinders translating into a uniform fluid at a constant speed large enough so that the flow seen in the body-fixed frame is steady and unseparated. The theorem relates thelift generated by an airfoil to the speed of the airfoil through the fluid, the density of the fluid and thecirculation around the airfoil. The circulation is defined as the line integral around a closed-loop enclosing the airfoil of the component of the velocity of the fluidtangent to the loop.[122] It is named afterMartin Kutta andNikolai Zhukovsky (or Joukowski) who first developed its key ideas in the early 20th century. Kutta–Joukowski theorem is aninviscid theory, but it is a good approximation for real viscous flow in typical aerodynamic applications.[123]

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  • Landerspacecraft designed to soft-land intact or almost undamaged on the surface of acelestial body and eventually take-off from it
  • Landing – is the last part of aflight, where anaircraft, orspacecraft returns to the ground. When the flying object returns to water, the process is calledalighting, although it is commonly called "landing", "touchdown"a or "splashdown" as well. A normal aircraft flight would include several parts of flight includingtaxi,takeoff,climb,cruise,descent and landing.
  • Landing gear – is the undercarriage of anaircraft orspacecraft and may be used for eithertakeoff orlanding. For aircraft it is generally needed for both. Also, for aircraft, the landing gear supports the craft when it is not flying, allowing it to take off, land, and taxi without damage. Wheeled landing gear is the most common, withskis orfloats needed to operate from snow/ice/water and skids for vertical operation on land. Faster aircraft have retractable undercarriages, which fold away during flight to reducedrag.
  • Lagrangian mechanics – Introduced by the Italian-French mathematician and astronomerJoseph-Louis Lagrange in 1788,Lagrangian mechanics is a formulation ofclassical mechanics and is founded on thestationary action principle.
Lagrangian mechanics defines a mechanical system to be a pair(M,L){\displaystyle (M,L)} of aconfiguration spaceM{\displaystyle M} and a smooth functionL=L(q,v,t){\displaystyle L=L(q,v,t)} calledLagrangian. By convention,L=TV,{\displaystyle L=T-V,} whereT{\displaystyle T} andV{\displaystyle V} are thekinetic andpotential energy of the system, respectively. HereqM,{\displaystyle q\in M,} andv{\displaystyle v} is the velocity vector atq{\displaystyle q}(v{\displaystyle (v} is tangential toM).{\displaystyle M).} (For those familiar withtangent bundles,L:TM×RtR,{\displaystyle L:TM\times \mathbb {R} _{t}\to \mathbb {R} ,} andvTqM).{\displaystyle v\in T_{q}M).}
Given the time instantst1{\displaystyle t_{1}} andt2,{\displaystyle t_{2},} Lagrangian mechanics postulates that a smooth pathx0:[t1,t2]M{\displaystyle x_{0}:[t_{1},t_{2}]\to M} describes the time evolution of the given system if and only ifx0{\displaystyle x_{0}} is astationary point of theaction functional
S[x]=deft1t2L(x(t),x˙(t),t)dt.{\displaystyle {\cal {S}}[x]\,{\stackrel {\text{def}}{=}}\,\int _{t_{1}}^{t_{2}}L(x(t),{\dot {x}}(t),t)\,dt.}
IfM{\displaystyle M} is an open subset ofRn{\displaystyle \mathbb {R} ^{n}} andt1,{\displaystyle t_{1},}t2{\displaystyle t_{2}} are finite, then the smooth pathx0{\displaystyle x_{0}} is a stationary point ofS{\displaystyle {\cal {S}}} if all its directional derivatives atx0{\displaystyle x_{0}} vanish, i.e., for every smoothδ:[t1,t2]Rn,{\displaystyle \delta :[t_{1},t_{2}]\to \mathbb {R} ^{n},}
δS =def ddε|ε=0S[x0+εδ]=0.{\displaystyle \delta {\cal {S}}\ {\stackrel {\text{def}}{=}}\ {\frac {d}{d\varepsilon }}{\Biggl |}_{\varepsilon =0}{\cal {S}}\left[x_{0}+\varepsilon \delta \right]=0.}
The functionδ(t){\displaystyle \delta (t)} on the right-hand side is calledperturbation orvirtual displacement. The directional derivativeδS{\displaystyle \delta {\cal {S}}} on the left is known asvariation in physics andGateaux derivative in mathematics.
Lagrangian mechanics has been extended to allow for non-conservative forces.

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p=mv.{\displaystyle \mathbf {p} =m\mathbf {v} .}
In theInternational System of Units (SI), theunit of measurement of momentum is thekilogrammetre per second (kg⋅m/s), which is equivalent to thenewton-second.
  • Momentum wheel
  • Monopropellant rocket – ormonochemical rocket, is arocket that uses a singlechemical as itspropellant.
  • Motion – Inphysics, motion is the phenomenon in which an object changes itsposition. Motion is mathematically described in terms ofdisplacement,distance,velocity,acceleration,speed, andtime. The motion of a body is observed by attaching aframe of reference to an observer and measuring the change in position of the body relative to that frame with change in time. The branch of physics describing the motion of objects without reference to its cause iskinematics; the branch studying forces and their effect on motion isdynamics.
  • Multistage rocket – orstep rocket[153] is alaunch vehicle that uses two or morerocketstages, each of which contains its ownengines andpropellant. Atandem orserial stage is mounted on top of another stage; aparallel stage is attached alongside another stage. The result is effectively two or more rockets stacked on top of or attached next to each other. Two-stage rockets are quite common, but rockets with as many as five separate stages have been successfully launched.

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The Navier–Stokes equations mathematically expressconservation of momentum andconservation of mass forNewtonian fluids. They are sometimes accompanied by anequation of state relatingpressure,temperature anddensity.[154] They arise from applyingIsaac Newton's second law tofluid motion, together with the assumption that thestress in the fluid is the sum of adiffusingviscous term (proportional to thegradient of velocity) and apressure term—hence describingviscous flow. The difference between them and the closely relatedEuler equations is that Navier–Stokes equations take viscosity into account while the Euler equations model onlyinviscid flow. As a result, the Navier–Stokes are aparabolic equation and therefore have better analytic properties, at the expense of having less mathematical structure (e.g. they are nevercompletely integrable).
A newton is defined as 1 kg⋅m/s2, which is the force which gives a mass of 1 kilogram an acceleration of 1 metre per second, per second.
This is a generalphysical law derived fromempirical observations by whatIsaac Newton calledinductive reasoning.[158] It is a part ofclassical mechanics and was formulated in Newton's workPhilosophiæ Naturalis Principia Mathematica ("thePrincipia"), first published on 5 July 1687. When Newton presented Book 1 of the unpublished text in April 1686 to theRoyal Society,Robert Hooke made a claim that Newton had obtained the inverse square law from him.
In today's language, the law states that everypointmass attracts every other point mass by aforce acting along theline intersecting the two points. The force isproportional to theproduct of the two masses, and inversely proportional to thesquare of the distance between them.[159]
The equation for universal gravitation thus takes the form:
F=Gm1m2r2,{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},}
whereF is the gravitational force acting between two objects,m1 andm2 are the masses of the objects,r is the distance between thecenters of their masses, andG is thegravitational constant.
Law 1. A body continues in its state of rest, or in uniform motion in a straight line, unless acted upon by a force.
Law 2. A body acted upon by a force moves in such a manner that the time rate of change ofmomentum equals the force.
Law 3. If two bodies exert forces on each other, these forces are equal in magnitude and opposite in direction.
The three laws of motion were first stated byIsaac Newton in hisPhilosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687.[161] Newton used them to explain and investigate the motion of many physical objects and systems, which laid the foundation for Newtonian mechanics.[162]
  • Nose cone design – Given the problem of theaerodynamicdesign of thenose cone section of any vehicle or body meant to travel through acompressible fluid medium (such as arocket oraircraft,missile orbullet), an important problem is the determination of thenose cone geometrical shape for optimum performance. For many applications, such a task requires the definition of asolid of revolution shape that experiences minimal resistance to rapid motion through such a fluid medium.
  • Nozzle – is a device designed to control the direction or characteristics of afluid flow (especially to increase velocity) as it exits (or enters) an enclosed chamber orpipe. A nozzle is often a pipe or tube of varying cross-sectional area, and it can be used to direct or modify the flow of a fluid (liquid orgas). Nozzles are frequently used to control the rate of flow, speed, direction, mass, shape, and/or the pressure of the stream that emerges from them. In a nozzle, the velocity of fluid increases at the expense of its pressure energy.

O

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P

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Define perpendicular axesx{\displaystyle x},y{\displaystyle y}, andz{\displaystyle z} (which meet at originO{\displaystyle O}) so that the body lies in thexy{\displaystyle xy} plane, and thez{\displaystyle z} axis is perpendicular to the plane of the body. LetIx,Iy andIz be moments of inertia about axisx,y,z respectively. Then the perpendicular axis theorem states that[174]
Iz=Ix+Iy{\displaystyle I_{z}=I_{x}+I_{y}}
This rule can be applied with theparallel axis theorem and thestretch rule to find polar moments of inertia for a variety of shapes.
If a planar object (or prism, by thestretch rule) has rotational symmetry such thatIx{\displaystyle I_{x}} andIy{\displaystyle I_{y}} are equal,[175]
then the perpendicular axes theorem provides the useful relationship:
Iz=2Ix=2Iy{\displaystyle I_{z}=2I_{x}=2I_{y}}

Q

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R

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S

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T

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The equation itself is:[184]
vf2=vi2+2aΔx{\displaystyle v_{f}^{2}=v_{i}^{2}+2a\Delta x\,}
where
This equation is valid along any axis on which the acceleration is constant.

U

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  • UFO – An unidentified flying object is any perceived aerial phenomenon that cannot be immediately identified or explained. On investigation, most UFOs areidentified as known objects or atmospheric phenomena, while a small number remain unexplained.

V

[edit]
Velocity is a physicalvectorquantity; both magnitude and direction are needed to define it. Thescalarabsolute value (magnitude) of velocity is calledspeed, being a coherent derived unit whose quantity is measured in theSI (metric system) asmetres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object is said to be undergoing anacceleration.

W

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  • Wave drag – Inaeronautics, wave drag is a component of theaerodynamic drag on aircraft wings and fuselage, propeller blade tips andprojectiles moving attransonic andsupersonic speeds, due to the presence ofshock waves.[194] Wave drag is independent ofviscous effects,[195] and tends to present itself as a sudden and dramatic increase in drag as the vehicle increases speed to theCritical Mach number. It is the sudden and dramatic rise of wave drag that leads to the concept of asound barrier.
  • Weight – Inscience andengineering, theweight of an object is theforce acting on the object due togravity.[196][197][198]
  • Weight function – is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is aweighted sum orweighted average. Weight functions occur frequently instatistics andanalysis, and are closely related to the concept of ameasure. Weight functions can be employed in both discrete and continuous settings. They can be used to construct systems of calculus called "weighted calculus"[199] and "meta-calculus".[200]
  • Wind tunnels – are large tubes with air blowing through them which are used to replicate the interaction between air and an object flying through the air or moving along the ground. Researchers use wind tunnels to learn more about how an aircraft will fly.NASA uses wind tunnels to testscale models of aircraft and spacecraft. Some wind tunnels are large enough to contain full-size versions of vehicles. The wind tunnel moves air around an object, making it seem as if the object is flying.
  • Wing – is a type offin that produceslift while moving through air or some otherfluid. Accordingly, wings havestreamlinedcross-sections that are subject toaerodynamic forces and act asairfoils. A wing'saerodynamic efficiency is expressed as itslift-to-drag ratio. The lift a wing generates at a given speed andangle of attack can be one to twoorders of magnitude greater than the totaldrag on the wing. A high lift-to-drag ratio requires a significantly smallerthrust to propel the wings through the air at sufficient lift.
  • Wright Flyer – TheWright Flyer (theKitty Hawk,[201][202] also known asFlyer I or1903Flyer) made the first sustained flight by a mannedheavier-than-air powered and controlled aircraft—anairplane—on 17 December 1903.[203] Invented and flown byOrville and Wilbur Wright, it marked the beginning of the"pioneer era" of aviation.
  • Wright Glider – TheWright brothers designed, built and flew a series of three mannedgliders in 1900–1902 as they worked towards achieving poweredflight. They also made preliminary tests with akite in 1899. In 1911 Orville conducted tests with a much more sophisticated glider. Neither the kite nor any of the gliders were preserved, but replicas of all have been built.

X

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Y

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Z

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See also

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References

[edit]
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  1. ^Geostationary orbit andGeosynchronous (equatorial) orbit are used somewhat interchangeably in sources.
  2. ^"Newtonian constant of gravitation" is the name introduced forG by Boys (1894). Use of the term by T.E. Stern (1928) was misquoted as "Newton's constant of gravitation" inPure Science Reviewed for Profound and Unsophisticated Students (1930), in what is apparently the first use of that term. Use of "Newton's constant" (without specifying "gravitation" or "gravity") is more recent, as "Newton's constant" was alsoused for theheat transfer coefficient inNewton's law of cooling, but has by now become quite common, e.g.Calmet et al,Quantum Black Holes (2013), p. 93; P. de Aquino,Beyond Standard Model Phenomenology at the LHC (2013), p. 3. The name "Cavendish gravitational constant", sometimes "Newton–Cavendish gravitational constant", appears to have been common in the 1970s to 1980s, especially in (translations from) Soviet-era Russian literature, e.g. Sagitov (1970 [1969]),Soviet Physics: Uspekhi 30 (1987), Issues 1–6, p. 342 [etc.]."Cavendish constant" and "Cavendish gravitational constant" is also used in Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, "Gravitation", (1973), 1126f. Colloquial use of "Big G", as opposed to "little g" for gravitational acceleration dates to the 1960s (R.W. Fairbridge,The encyclopedia of atmospheric sciences and astrogeology, 1967, p. 436; note use of "Big G's" vs. "little g's" as early as the 1940s of theEinstein tensorGμν vs. themetric tensorgμν,Scientific, medical, and technical books published in the United States of America: a selected list of titles in print with annotations: supplement of books published 1945–1948, Committee on American Scientific and Technical Bibliography National Research Council, 1950, p. 26).
  3. ^Cavendish determined the value ofG indirectly, by reporting a value for theEarth's mass, or the average density of Earth, as5.448 g⋅cm−3.
  4. ^ISO 15919:Bhāratīya Antarikṣ Anusandhān SaṅgaṭhanBhāratīya Antrikṣ Anusandhān Saṅgaṭhan
  5. ^CNSA (China),ESA (most of Europe), ISRO, (India),JAXA (Japan),NASA (United States) andRoscosmos (Russia) are space agencies with full launch capabilities.
  1. ^It was shown separately that separated spherically symmetrical masses attract and are attractedas if all their mass were concentrated at their centers.
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