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Roll, Pitch, And Yaw
The Euler angles
Euler angles
are three angles introduced by Leonhard Euler
Leonhard Euler
to describe the orientation of a rigid body with respect to a fixed coordinate system.[1] They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general basis in 3-dimensional linear algebra. Any orientation can be achieved by composing three elemental rotations, i.e. rotations about the axes of a coordinate system. Euler angles can be defined by three of these rotations
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Mathematics
Mathematics
Mathematics
(from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity,[1] structure,[2] space,[1] and change.[3][4][5] It has no generally accepted definition.[6][7] Mathematicians seek out patterns[8][9] and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist
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Banked Turn
A banked turn (or banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a road or railroad this is usually due to the roadbed having a transverse down-slope towards the inside of the curve. The bank angle is the angle at which the vehicle is inclined about its longitudinal axis with respect to the horizontal.Contents1 Turn on flat surfaces 2 Frictionless banked turn 3 Banked turn
Banked turn
with friction 4 Banked turn
Banked turn
in aeronautics 5 See also 6 Notes 7 References 8 External linksTurn on flat surfaces[edit] If the bank angle is zero, the surface is flat and the normal force is vertically upward. The only force keeping the vehicle turning on its path is friction, or traction
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Nutation
Nutation
Nutation
(from Latin
Latin
nūtātiō, "nodding, swaying") is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism. In an appropriate reference frame it can be defined as a change in the second Euler angle
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Rotation
A rotation is a circular movement of an object around a center (or point) of rotation. A three-dimensional object can always be rotated around an infinite number of imaginary lines called rotation axes (/ˈæksiːz/ AK-seez). If the axis passes through the body's center of mass, the body is said to rotate upon itself, or spin. A rotation about an external point, e.g. the Earth
Earth
about the Sun, is called a revolution or orbital revolution, typically when it is produced by gravity. The axis is called a pole.Contents1 Mathematics 2 Astronomy2.1 Rotation
Rotation
and revolution 2.2 Retrograde rotation3 Physics3.1 Cosmological principle 3.2 Euler rotations4 Flight dynamics 5 Amusement rides 6 Sports 7 Fixed axis vs
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Top
A spinning top is a toy designed to spin rapidly on the ground, the motion of which causes it to remain precisely balanced on its tip because of its rotational inertia. Such toys have existed since antiquity. Traditionally tops were constructed of wood, sometimes with an iron tip, and would be set in motion by aid of a string or rope coiled around its axis which, when pulled quickly, caused a rapid unwinding that would set the top in motion
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Peter Guthrie Tait
Peter Guthrie Tait FRSE
FRSE
(28 April 1831 – 4 July 1901) was a Scottish mathematical physicist, best known for the mathematical physics textbook Treatise on Natural Philosophy, which he co-wrote with Kelvin, and his early investigations into knot theory, which contributed to the eventual formation of topology as a mathematical discipline. His name is known in graph theory mainly for Tait's conjecture.Contents1 Early years 2 Middle years 3 Later years3.1 Chronological order of books4 Private life 5 Artistic recognition 6 References 7 External linksEarly years[edit] He was born in Dalkeith
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George H. Bryan
George Hartley Bryan FRS[1] (1 March 1864, Cambridge
Cambridge
– 13 October 1928, Bordighera) was an English applied mathematician who was an authority on thermodynamics and aeronautics. He was educated at Peterhouse College, Cambridge, obtaining his BA in 1886 (as 5th wrangler), MA in 1890, and DSc in 1896.[2] He was a professor at University College of North Wales, and is generally credited with developing the modern mathematical treatment of the motion of airplanes in flight as rigid bodies with six degrees of freedom. Aside from minor differences in notation, Bryan's 1911 equations are the same as those used today to evaluate modern aircraft
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Axes Conventions
In ballistics and flight dynamics, axes conventions are standardized ways of establishing the location and orientation of coordinate axes for use as a frame of reference. Mobile objects are normally tracked from an external frame considered fixed. Other frames can be defined on those mobile objects to deal with relative positions for other objects. Finally, attitudes or orientations can be described by a relationship between the external frame and the one defined over the mobile object. The orientation of a vehicle is normally referred to as attitude. It is described normally by the orientation of a frame fixed in the body relative to a fixed reference frame
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Aircraft Principal Axes
An aircraft in flight is free to rotate in three dimensions: yaw, nose left or right about an axis running up and down; pitch, nose up or down about an axis running from wing to wing; and roll, rotation about an axis running from nose to tail. The axes are alternatively designated as lateral, vertical, and longitudinal. These axes move with the vehicle and rotate relative to the Earth along with the craft. These definitions were analogously applied to spacecraft when the first manned spacecraft were designed in the late 1950s. These rotations are produced by torques (or moments) about the principal axes. On an aircraft, these are intentionally produced by means of moving control surfaces, which vary the distribution of the net aerodynamic force about the vehicle's center of mass. Elevators (moving flaps on the horizontal tail) produce pitch, a rudder on the vertical tail produces yaw, and ailerons (flaps on the wings that move in opposing directions) produce roll
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Deutsches Institut Für Normung
Deutsches Institut für Normung
Deutsches Institut für Normung
e.V. (DIN; in English, the German Institute for Standardization) is the German national organization for standardization and is the German ISO member body. DIN is a German Registered Association (e.V.) headquartered in Berlin. There are currently around thirty thousand DIN Standards, covering nearly every field of technology.Contents1 History 2 DIN standard designation 3 Examples of DIN standards 4 See also 5 External linksHistory[edit] Founded in 1917 as the Normenausschuß der deutschen Industrie (NADI, "Standardisation Committee of German Industry"), the NADI was renamed Deutscher Normenausschuß (DNA, "German Standardisation Committee") in 1926 to reflect that the organization now dealt with standardization issues in many fields; viz., not just for industrial products
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Bearing (navigation)
In navigation bearing may refer, depending on the context, to any of: (A) the direction or course of motion itself[citation needed]; (B) the direction of a distant object relative to the current course (or the "change" in course that would be needed to get to that distant object); or (C), the angle away from North of a distant point as observed at the current point.[citation needed] Absolute bearing
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
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Elevation (ballistics)
In ballistics, the elevation is the angle between the horizontal plane and the direction of the barrel of a gun, mortar or heavy artillery. Originally, elevation was a linear measure of how high the gunners had to physically lift the muzzle of a gun up from the gun carriage to hit targets at a certain distance.Contents1 Pre-WWI and WWI 2 WWII and beyond 3 See also 4 ReferencesPre-WWI and WWI[edit] Though early 20th-century firearms were relatively easy to fire, artillery was not. Before and during World War I, the only way to effectively fire artillery was plotting points on a plane. Most artillery units seldom employed their cannons in small numbers. Instead of using pin-point artillery firing they used old means of "fire for effect" using artillery en masse. This tactic was employed successfully by past armies. But changes have been made since past wars and in World War I, artillery was more accurate than before, although not as accurate as artillery one century newer
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Physics
Physics
Physics
(from Ancient Greek: φυσική (ἐπιστήμη), translit. physikḗ (epistḗmē), lit. 'knowledge of nature', from φύσις phýsis "nature"[1][2][3]) is the natural science that studies matter[4] and its motion and behavior through space and time and that studies the related entities of energy and force.[5] Physics
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Yaw (rotation)
A yaw rotation is a movement around the yaw axis of a rigid body that changes the direction it is pointing, to the left or right of its direction of motion. The yaw rate or yaw velocity of a car, aircraft, projectile or other rigid body is the angular velocity of this rotation, or rate of change of the heading angle when the aircraft is horizontal. It is commonly measured in degrees per second or radians per second. Another important concept is the yaw moment, or yawing moment, which is the component of a torque about the yaw axis.Contents1 Measurement 2 Yaw rate control 3 Road vehicles 4 Relationship with other rotation systems 5 History 6 See also 7 ReferencesMeasurement[edit] Yaw velocity can be measured by measuring the ground velocity at two geometrically separated points on the body, or by a gyroscope, or it can be synthesized from accelerometers and the like
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Pitching Moment
In aerodynamics, the pitching moment on an airfoil is the moment (or torque) produced by the aerodynamic force on the airfoil if that aerodynamic force is considered to be applied, not at the center of pressure, but at the aerodynamic center of the airfoil. The pitching moment on the wing of an airplane is part of the total moment that must be balanced using the lift on the horizontal stabilizer.[1] More generally, a pitching moment is any moment acting on the pitch axis of a moving body. The lift on an airfoil is a distributed force that can be said to act at a point called the center of pressure. However, as angle of attack changes on a cambered airfoil, there is movement of the center of pressure forward and aft. This makes analysis difficult when attempting to use the concept of the center of pressure
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