angular displacement

• 偏位角度

WordNet

1. (chemistry) a reaction in which an elementary substance displaces and sets free a constituent element from a compound (同)displacement reaction
2. (psychiatry) a defense mechanism that transfers affect or reaction from the original object to some more acceptable one
3. to move something from its natural environment (同)deracination
4. act of removing from office or employment
5. measured by an angle or by the rate of change of an angle; "angular momentum"
6. having angles or an angular shape (同)angulate

PrepTutorEJDIC

1. とって代わること,置き換え / 解職,罷免 / 排水量
2. かどのある,とがった / かどから成る;かどを成す;角度で測った / 骨ばった,やせこけた / (態度が)ぎこちない,堅苦しい

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/04/28 18:17:12」(JST)

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Classical mechanics
Second law of motion
History Timeline
Branches Applied Celestial Continuum Dynamics Kinematics Kinetics Statics Statistical
Fundamentals Acceleration Angular momentum Couple D'Alembert's principle Energy kinetic potential Force Frame of reference Impulse Inertia / Moment of inertia Mass Mechanical power Mechanical work Moment Momentum Space Speed Time Torque Velocity Virtual work
Formulations Newton's laws of motion Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of motion Udwadia–Kalaba equation
Core topics Damping (ratio) Displacement Equations of motion Euler's laws of motion Fictitious force Friction Harmonic oscillator Inertial / Non-inertial reference frame Mechanics of planar particle motion Motion (linear) Newton's law of universal gravitation Newton's laws of motion Relative velocity Rigid body dynamics Euler's equations Simple harmonic motion Vibration
Rotation Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational speed Angular acceleration / displacement / frequency / velocity
Scientists Galileo Newton Kepler Horrocks Halley Euler d'Alembert Clairaut Lagrange Laplace Hamilton Poisson Daniel Bernoulli Johann Bernoulli Cauchy

Rotation of a rigid object P about a fixed object about a fixed axis O.

Angular displacement of a body is the angle in radians (degrees, revolutions) through which a point or line has been rotated in a specified sense about a specified axis. When an object rotates about its axis, the motion cannot simply be analyzed as a particle, since in circular motion it undergoes a changing velocity and acceleration at any time (t). When dealing with the rotation of an object, it becomes simpler to consider the body itself rigid. A body is generally considered rigid when the separations between all the particles remains constant throughout the objects motion, so for example parts of its mass are not flying off. In a realistic sense, all things can be deformable, however this impact is minimal and negligible. Thus the rotation of a rigid body over a fixed axis is referred to as rotational motion.

Example

In the example illustrated to the right (or above in some mobile versions) , a particle on object P at a fixed distance r from the origin, O, rotating counterclockwise. It becomes important to then represent the position of particle P in terms of its polar coordinates (r, θ). In this particular example, the value of θ is changing, while the value of the radius remains the same. (In rectangular coordinates (x, y) both x and y vary with time). As the particle moves along the circle, it travels an arc length s, which becomes related to the angular position through the relationship:

$s=r\theta \,$

Measurements of angular displacement

Angular displacement may be measured in radians or degrees. If using radians, it provides a very simple relationship between distance traveled around the circle and the distance r from the centre.

For example if an object rotates 360 degrees around a circle of radius r, the angular displacement is given by the distance traveled around the circumference - which is 2πr divided by the radius: which easily simplifies to . Therefore 1 revolution is radians.

When object travels from point P to point Q, as it does in the illustration to the left, over the radius of the circle goes around a change in angle. which equals the Angular Displacement.

Three dimensions

In three dimensions, angular displacement is an entity with a direction and a magnitude. The direction specifies the axis of rotation, which always exists by virtue of the Euler's rotation theorem; the magnitude specifies the rotation in radians about that axis (using the right-hand rule to determine direction).

Despite having direction and magnitude, angular displacement is not a vector because it does not obey the commutative law for addition.

Matrix notation

Given that any frame in the space can be described by a rotation matrix, the displacement among them can also be described by a rotation matrix. Being and two matrices, the angular displacement matrix between them can be obtained as

References

See also

• Second moment of area
• Linear elasticity
• Infinitesimal rotation
• Angular distance
• Angular velocity

UpToDate Contents

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English Journal

• Motor adaptation to prosthetic cycling in people with trans-tibial amputation.

• Lee Childers W1, Prilutsky BI2, Gregor RJ3.
• Journal of biomechanics.J Biomech.2014 Jul 18;47(10):2306-13. doi: 10.1016/j.jbiomech.2014.04.037. Epub 2014 Apr 26.
• The neuromusculoskeletal system interacts with the external environment via end-segments, e.g. feet. A person with trans-tibial amputation (TTAmp) has lost a foot and ankle; hence the residuum with prosthesis becomes the new end-segment. We investigated changes in kinetics and muscle activity in TTA
• PMID 24818794

• Gaussian semiflexible rings under angular and dihedral restrictions.

• Dolgushev M1, Guérin T2, Blumen A1, Bénichou O2, Voituriez R2.
• The Journal of chemical physics.J Chem Phys.2014 Jul 7;141(1):014901. doi: 10.1063/1.4885445.
• Semiflexible polymer rings whose bonds obey both angular and dihedral restrictions [M. Dolgushev and A. Blumen, J. Chem. Phys. 138, 204902 (2013)], are treated under exact closure constraints. This allows us to obtain semianalytic results for their dynamics, based on sets of Langevin equations. The
• PMID 25005305

• Biomechanical effects of pedicle screw fixation on adjacent segments.

• Kyaw TA1, Wang Z, Sakakibara T, Yoshikawa T, Inaba T, Kasai Y.
• European journal of orthopaedic surgery & traumatology : orthopédie traumatologie.Eur J Orthop Surg Traumatol.2014 Jul;24 Suppl 1:283-7. doi: 10.1007/s00590-014-1416-1. Epub 2014 Jan 22.
• Various biomechanical investigations have attempted to clarify the aetiology of adjacent segment disease (ASD). However, no biomechanical study has examined in detail the deformation behaviour of the adjacent segments when both pure torque and an angular displacement load are applied to the vertebra
• PMID 24449003

Japanese Journal

• <no title>

• Li Zhen,Mitsuoka Muneshi,Inoue Eiji,Okayasu Takashi,Hirai Yasumaru
• Journal of the Faculty of Agriculture, Kyushu University 59(2), 339-343, 2014-08-29
• … Dynamic behavior of the tractor was described by capturing the motion of its center of gravity, which includes vertical displacement, angle, and angular acceleration for the pitching and rolling phenomena. …
• NAID 120005472186

• ハイブリッド支持式回転型ジャイロへの不つり合い補償の適用

• 秋山 智広,水野 毅,高崎 正也,石野 裕二
• 日本AEM学会誌 22(2), 220-225, 2014
• … However, one of the problems is that an oscillating component due to unbalance appears in the estimated angular velocity because the estimation is based on the control currents for regulating the relative displacement of the holder to the stator. …
• NAID 130004698698

• Differences in trunk rotation during baseball batting between skilled players and unskilled novices

• Nakata Hiroki,Miura Akito,Yoshie Michiko,Higuchi Takatoshi,Kudo Kazutoshi
• The Journal of Physical Fitness and Sports Medicine 3(4), 457-466, 2014
• … The maximum angle during the backswing, angle at bat-ball impact, and angular displacement during the forward swing were analyzed for data on upper torso, pelvis, and torso-pelvis interaction (trunk twist) angles. … Statistical analysis revealed that angular displacements in the upper torso, pelvis, and torso-pelvis interaction were significantly larger in skilled players than in unskilled novices (p < …
• NAID 130004698668

Related Links

• Angular displacement | Define Angular displacement at ...

Angular displacement definition, the amount of rotation of a point, line, or body in a specified direction about an axis. See more. Thesaurus Translate Puzzles & Games Word of the Day Blog Slideshows Apps by Dictionary Log In ...

• Angular displacement - definition of angular displacement by ...

angular displacement n. An angle crossed by a moving body with respect to some reference point. angular displacement n 1. (General Physics) physics the angle through ... Offering precise 12-bit resolution over a full 0-360A rotation ...

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関連記事	「displacement」「angular」

「displacement」

　　[★]

• n.

• 置換、置換術、転置

関

displace、replace、replacement、substitute、substitution、substitutional、transpose

　 　 　 　 　

「angular」

　　[★]

• 角の

関

angle、corner、horn