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`MOTHERSON
`EXHIBIT 1009
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`MOTHERSON
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`EXHIBIT 1009
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`

`

`3/30/2020
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`Aircraft principal axes - Wikipedia
`
`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 vertical, transverse, and longitudinal respectively.
`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 gravity. 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. On a spacecraft, the
`moments are usually produced by a reaction control system consisting of small rocket thrusters used to
`apply asymmetrical thrust on the vehicle.
`
`Yaw, pitch and roll in an aircraft
`
`Contents
`Principal axes
`Vertical axis (yaw)
`Transverse axis (pitch)
`Longitudinal axis (roll)
`Relationship with other systems of axes
`History
`See also
`References
`External links
`
`Principal axes
`
`Normal axis, or yaw axis — an axis drawn from top to bottom, and perpendicular to the other two
`axes. Parallel to the fuselage station.
`Transverse axis, lateral axis, or pitch axis — an axis running from the pilot's left to right in piloted
`aircraft, and parallel to the wings of a winged aircraft. Parallel to the buttock line.
`Longitudinal axis, or roll axis — an axis drawn through the body of the vehicle from tail to nose in the
`normal direction of flight, or the direction the pilot faces. Parallel to the waterline.
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`https://en.wikipedia.org/wiki/Aircraft_principal_axes
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`Aircraft principal axes - Wikipedia
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`Yaw/heading, pitch and roll angles and associated vertical (down),
`transverse and longitudinal axes
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`3/30/2020
`Normally, these axes are represented by
`the letters X, Y and Z in order to compare
`them with some reference frame, usually
`named x, y, z. Normally, this is made in
`such a way that the X is used for the
`longitudinal axis, but there are other
`possibilities to do it.
`
`Vertical axis (yaw)
`
`The yaw axis has its origin at the center of
`gravity and is directed towards the bottom
`of the aircraft, perpendicular to the wings
`and to the fuselage reference line. Motion
`about this axis is called yaw. A positive
`yawing motion moves the nose of the
`aircraft to the right.[1][2] The rudder is the
`primary control of yaw.[3]
`
`The term yaw was originally applied in
`sailing, and referred to the motion of an
`unsteady ship rotating about its vertical
`axis. Its etymology is uncertain.
`
`Transverse axis (pitch)
`
`The pitch axis (also called transverse or
`lateral axis[4]) has its origin at the center
`of gravity and is directed to the right,
`parallel to a line drawn from wingtip to
`wingtip. Motion about this axis is called
`pitch. A positive pitching motion raises
`the nose of the aircraft and lowers the tail.
`The elevators are the primary control of
`pitch.[3]
`
`Longitudinal axis (roll)
`
`The roll axis (or longitudinal axis[4]) has its origin at the
`center of gravity and is directed forward, parallel to the fuselage
`reference line. Motion about this axis is called roll. An angular
`displacement about this axis is called bank.[3] A positive rolling
`motion lifts the left wing and lowers the right wing. The pilot
`rolls by increasing the lift on one wing and decreasing it on the
`other. This changes the bank angle. The ailerons are the primary
`control of bank. The rudder also has a secondary effect on
`bank.[5]
`
`The position of all three axes, with the
`right-hand rule for its rotations
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`https://en.wikipedia.org/wiki/Aircraft_principal_axes
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`Motherson Innovations v. Magna Mirrors
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`3/30/2020
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`Aircraft principal axes - Wikipedia
`
`Relationship with other systems of axes
`
`These axes are related to the principal axes of inertia, but are not the same. They are geometrical
`symmetry axes, regardless of the mass distribution of the aircraft.
`
`In aeronautical and aerospace engineering intrinsic rotations around these axes are often called Euler
`angles, but this conflicts with existing usage elsewhere. The calculus behind them is similar to the
`Frenet–Serret formulas. Performing a rotation in an intrinsic reference frame is equivalent to right-
`multiplying its characteristic matrix (the matrix that has the vector of the reference frame as columns) by
`the matrix of the rotation.
`History
`
`The first aircraft to demonstrate active control about all three axes was the Wright brothers' 1902
`glider.[6]
`See also
`
`Aerodynamics
`Aircraft flight control system
`Euler angles
`Fixed-wing aircraft
`Flight control surfaces
`Flight dynamics
`Flight dynamics (fixed-wing aircraft)
`Moving frame
`Panning (camera)
`Six degrees of freedom
`Screw theory
`Triad method
`
`References
`
`1. "Yaw axis" (http://www.answers.com/topic/yaw-axis). Retrieved 2008-07-31.
`2. "Specialty Definition: YAW AXIS" (https://archive.is/20121008001023/http://www.websters-online-dict
`ionary.org/ya/yaw+axis.html). Archived from the original (http://www.websters-online-dictionary.org/y
`a/yaw+axis.html) on 2012-10-08. Retrieved 2008-07-31.
`3. Clancy, L.J. (1975) Aerodynamics Pitman Publishing Limited, London ISBN 0-273-01120-0, Section
`16.6
`4. "MISB Standard 0601" (http://www.gwg.nga.mil/misb//docs/standards/ST0601.8.pdf) (PDF). Motion
`Imagery Standards Board (MISB). Retrieved 1 May 2015. Also at File:MISB Standard 0601.pdf.
`5. FAA (2004). Airplane Flying Handbook. Washington D.C.:U.S. Department of Transportation, Federal
`Aviation Administration, ch 4, p 2, FAA-8083-3A.
`6. "Aircraft rotations" (http://www.grc.nasa.gov/WWW/K-12/airplane/rotations.html). Archived (https://we
`b.archive.org/web/20080704135659/http://www.grc.nasa.gov/WWW/K-12/airplane/rotations.html)
`from the original on 4 July 2008. Retrieved 2008-08-04.
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`https://en.wikipedia.org/wiki/Aircraft_principal_axes
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`Motherson Innovations v. Magna Mirrors
`Motherson Exhibit 1009
`
`

`

`3/30/2020
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`External links
`
`Aircraft principal axes - Wikipedia
`
`Yaw Axis Control as a Means of Improving V/STOL Aircraft Performance. (https://web.archive.org/we
`b/20110717062743/http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD07
`49489)
`3D fast walking simulation of biped robot by yaw axis moment compensation (http://ieeexplore.ieee.o
`rg/Xplore/login.jsp?url=/iel5/9091/28850/01297903.pdf?temp=x)
`Flight control system for a hybrid aircraft in the yaw axis (https://web.archive.org/web/201106122048
`55/http://www.patentstorm.us/patents/6478262/claims.html)
`
`Retrieved from "https://en.wikipedia.org/w/index.php?title=Aircraft_principal_axes&oldid=926987181"
`
`This page was last edited on 19 November 2019, at 17:34 (UTC).
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`https://en.wikipedia.org/wiki/Aircraft_principal_axes
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`4/4
`
`Motherson Innovations v. Magna Mirrors
`Motherson Exhibit 1009
`
`