of rotation. Each part of the worm drive both the worm and the worm gear is rotating on its own axis. Rotationaround a fixedaxis is a special case of rotation al motion. The fixedaxis hypothesis exclude the possibility of a moving axis, and cannot describe such phenomena as nutation wobbling or precession . According to Euler s rotation theorem , simultaneous rotationaround more than one axis at the same time is impossible. If two rotations are forced at the same time, a new axis of rotation will appear. The kinematics and dynamics mechanics dynamics of rotationaround a fixedaxis of a rigid ... around a fixedaxis, than for general rotational motion. For these reasons, rotationaround a fixed ... around which the torque tends to cause rotation. To maintain rotationaround a fixedaxis, the total ... The simplest case of rotationaround a fixedaxis is that of constant angular speed. Then the total torque is zero. For the example of the Earth rotating around its axis, there is very little friction ... elliptic orbit s. The special case of circular orbit s is an example of a rotationaround a fixed ... free rotation of a rigid body they are entirely analogous to those of linear motion along a single fixed direction, which is not true for free rotation of a rigid body . The expressions for the kinetic ... from the axis of rotation. This is also the tangential component of acceleration it is tangential ... a distance math r math from the axis of rotation, the moment of inertia is given by math I mr 2. math ... is at position r from its axis of rotation. Mathematically, math boldsymbol tau mathbf r times mathbf ... points in the direction of the vector. The angular velocity vector also points along the axis of rotation ... points along the axis of rotation in the same direction that the angular velocity would point ... the axis has effect on the rotation, other forces and torques are compensated by the structure. Examples ... simple Axis of rotation uk ... more details
cyclic permutation Euler angles rigid body rotationaround a fixedaxisrotation group SO 3 rotation ... resembling a sphere rotating around an axis. A rotation is a circular motion circular movement of an object around a center or point geometry point of rotation . A Three dimensional space three dimensional object rotates always around an imaginary Line geometry line called a rotationaxis .... If a rotationaround a point or axis is followed by a second rotationaround the same point axis ..., the rotations around a point axis form a group mathematics group . However, a rotationaround a point or axis and a rotationaround a different point axis may result in something other than a rotation, e.g. a translation. Rotations around the x , y and z axes are called principal rotations . Rotationaround any axis can be performed by taking a rotationaround the x axis, followed by a rotationaround the y axis, and followed by a rotationaround the z axis. That is to say, any spatial rotation ... spin around on their axis. The rotation rate of planets in the solar system was first measured by tracking ... moves around another while rotation is used to mean the movement around an axis. Moons revolve around ... Main Rotation mathematics File Rotation illustration.png right thumb Rotation of a planar figure around ... thumb right Relations between rotationaxis, Orbital plane astronomy plane of orbit and axial ... perpendicular to the plane of the motion. If the axis of the rotation lies external of the body in question ... and or spin . The key distinction is simply where the axis of the rotation lies, either within ... of inertia . The angular velocity vector also describes the direction of the axis of rotation. Similarly ... axis, and parallel axes for each gondola, where the rotation is opposite, by gravity or mechanically ... axis. Many rides provide a combination of rotations about several axes. In Chair O Planes the rotation about the vertical axis is provided mechanically, while the rotation about the horizontal axis ... more details
wiktionary axisAxis may refer to In mathematics Axis of rotation , line aroundAxis of symmetry , a line ... by a Basis linear algebra basis vector in linear algebra In science Axis anatomy , the second cervical vertebra of the spine Axis genus Axis genus , a genus of deer Axis science festival , an annual technical festival held in Nagpur, India Axial tilt , the tilt of the axis on which the earth rotates, relative to the plane of the ecliptic Optical axis , a line of rotational symmetry in an optical system Optic axis of a crystal , the direction in which a ray of transmitted light suffers no birefringence Electrocardiographic axis The American Psychiatric Association organizes psychiatric diagnoses on a Diagnostic and Statistical Manual of Mental Disorders Multi axial system five axis system In geography Axis, Alabama , an unincorporated area In aerospace industry AXIS Flight Training Systems ... political spectrum Axis powers , Germany, Italy, Japan and their allies during World War II Axis of evil , U.S. President George W. Bush s description of Iran, Iraq, and North Korea In music Axis Bold as Love , album by The Jimi Hendrix Experience Axis Percussion , a US manufacturer of drum pedals and hardware Axis Records disambiguation , the name of several music labels Axis system , a system of harmonic analysis In fiction Axis novel , a science fiction novel by Robert Charles Wilson Universal Century AxisAxis , a colonized asteroid in the Gundam anime universe Axis Zeon, Zeon Neo Zeon movements inhabitants of the asteroid Axis in the Gundam anime universe Axis Chemicals , a fictional chemical plant in the first Batman film and in DC Comics In information technology Apache Axis , an open source Web service framework from the Apache Software Foundation Axis Communications , a Swedish manufacturer of IT equipment In manufacturing processes Multiaxis machining In communication Axis A division of the Saudi Telecom Company disambiguation de Axis es Eje fr Axis pl Axis simple Axis ... more details
Wiktionarypar rotationRotation is a circular motion of a body about a center. Rotation may also refer to Physics Differential rotation of objects Optical rotation polarization Rotational spectroscopy Mathematics Rotation mathematics Rotationaround a fixedaxis , a subset of rotation with more constraints Improper rotation producing an inversion The Curl mathematics curl of a vector field Bitwise rotation , a mathematical operator on bit patterns Music Rotation music , a term referring to the frequency of airplay of a particular song Rotation album , Cute Is What We Aim For s second studio album. Rotate song , a song off Capone N Noreaga s third album Channel 10 . Other Crop rotation , a farming practice Job rotation , a business management approach Stock rotation , a retail practice Rotation film , the film of that name. Rotation pool , a type of pocket billiards game In baseball pitching, the Glossary of baseball R rotationrotation is the group of starting pitchers for a team, and the order in which they pitch Robson Rotation , the practice of printing multiple ballots for an election, each having the candidates listed in a different order Clerkship medicine , also known as a rotation, referring in medical education to the later part of training where students spend time in a hospital environment, as opposed to receiving classroom instruction Rotation aviation refers to the act of lifting the nose off the runway during takeoff Display rotation , for the orientation of a page on the display device of a computer See also Rotation group disambiguation disambig cs Rotace rozcestn k de Rotation fr Rotation gl Rotaci n hom nimos hr Rotacija it Rotazione disambigua lb Rotatioun lt Rotacija nl Rotatie ja no Rotasjon nds Rotatschoon pl Obr t ujednoznacznienie pt Rota o ru sk Rot cia fi Rotaatio sv Rotation th ... more details
wiktionary fixedFixed may refer to Fixed EP Fixed EP , EP by Nine Inch Nails Fixed typeface , a collection of monospace bitmap fonts that is distributed with the X Window System Fixed, subjected to neutering Fixed point mathematics , a point that is mapped to itself by the function Fixed line telephone , a landline See also lookfrom intitle Fix disambiguation Fixer disambiguation Fixture disambiguation disambiguation ... more details
rotation s in space. In three dimensions it is an alternative to the Rotationaround a fixedaxisaxis of rotation , but unlike the axis of rotation it can be used in other dimensions, such as two ... like the Rotationaround a fixedaxisaxis of rotation in three dimensions, except rotations do not take ... no rotation takes place. In any rotation in three dimensions there is always a fixedaxis, the axis of rotation. The rotation can described by giving this axis, with the angle through which the rotation turns about it this is the axis angle representation of a rotation. The plane of rotation is the plane orthogonal to this axis, so the axis is a surface normal of the plane. The rotation then rotates this plane through the same angle as it rotates around the axis, that is everything in the plane ... has only one fixed point, the origin. Therefore an axis of rotation cannot be used in four dimensions ... the axis of rotation serves the same purpose and is the more established approach. The main use for them ... File PlaneRotation.svg thumb right 200px A three dimensional rotation, with an axis of rotation along the z axis and a plane of rotation in the xy plane In three dimensional space there are an infinite ... takes place about the z axis. The plane of rotation is the xy plane, so everything in that plane ... right 200px The Earth showing its axis and plane of rotation, both axial tilt inclined relative to the plane and perpendicular of Earth s orbit Another example is the Earth s rotation . The axis of rotation ..., an axis of rotation, so any description of a rotation in terms of a plane of rotation can be described in terms of an axis of rotation, and vice versa. But unlike the axis of rotation the plane generalises ... rotations simple rotation . In a simple rotation there is a fixed plane, and rotation can be said to take ... planes of rotation, no fixed planes, and the only fixed point is the origin. The rotation .... A simple rotation in n dimensions takes place about that is at a fixed distance from an nowrap ... more details
POV date April 2012 Infobox Company name PT AXIS Telekom Indonesia br AXIS logo type Private Company Private location Jakarta, Indonesia key people Erik Aas , CEO & President Director industry Telecommunications products AXIS parent homepage http www.axisworld.co.id AXIS launched its services in April 2008 and is available in more than 400 cities across all major islands of Indonesia, including Java, Sumatera, Kalimantan, Sulawesi, Bali and Lombok. Headquartered in Jakarta, AXIS is the fastest growing GSM and 3G mobile operator in Indonesia with more than 14 million mobile subscribers with a team of more than 700 highly motivated people. AXIS vision is to provide affordable communications to all Indonesians. In line with this vision, the company is aggressively expanding its services and coverage across the country. High speed mobile broadband services will be launched in major cities this year. Detailed information about AXIS is available at www.axisworld.co.id External links http www.axisworld.co.id AXIS official site http www.stc.com.sa Saudi Telecom official site http www.maxis.com.my Maxis Communications official site Indonesia mobile phone companies Asia company stub Category Mobile phone companies of Indonesia id Axis su Axis ... more details
Infobox musical artist See Wikipedia WikiProject Musicians name Axis Of image alt caption origin Portstewart , Northern Ireland genre Alternative rock br Hardcore punk Hardcore years active 2008&ndash present website http www.myspace.com axisof MySpace current members Ewen Friers br Niall Lawlor br Ethan Harman background group or band associated acts And So I Watch You From Afar Axis Of are a three piece Alternative Rock band based in Belfast , Northern Ireland . The band formed in 2008... History Axis Of formed in 2008, after various line up changes they released debut single Brobdingnagain in late 2009. Since early 2010 the band have enjoyed a rise in popularity, partly due to the release of their 2nd single Port Na Spaniagh , which was released along with a music video, available on Youtube . Following one of the bands UK tours in early 2010, Rock Sound Magazine dubbed them the most exciting band to come out of Northern Ireland, possibly ever & gave them a 9 10 rating for their live performance at a show in Newcastle upon Tyne Newcastle . As a result of this coverage the band were subsequently asked to take part in a Maida Vale Studios session in January 2010. Members Niall Lawlor Guitar, Vocals Ewen Friers Bass Guitar, Vocals Ethan Harman Drums External links http www.myspace.com axisof Official Myspace http www.facebook.com axisof Official Facebook http www.youtube.com watch?v 7VRJ6zGPeHc Port Na Spaniagh Music Video http www.bbc.co.uk programmes p00d7xm9 Maida Vale Session References http www.facebook.com topic.php?uid 168735498365&topic 13512 http www.bbc.co.uk programmes p00d7xm9 http issuu.com feilebelfast docs august 2010 http www.feilebelfast.com http www.drop d.ie legacy 1672 2017 Categories Category Articles created via the Article Wizard Category Rock music groups from Northern Ireland ... more details
rotation in four dimensions has only one fixed point, the centre of rotation, and no axis of rotation. Instead the rotation has two mutually orthogonal planes of rotation, each of which is fixed in the sense ...Image Rotation illustration2.svg right thumb Rotation of an object in two dimensions around a point math O. math In geometry and linear algebra , a rotation is a transformation geometry transformation in a plane or in space that describes the motion of a rigid body around a fixed point. A rotation is different from a translation mathematics translation , which has no fixed points, and from a reflection mathematics reflection , which flips the bodies it is transforming. A rotation and the above mentioned ... in a total motion that is a rotationaround the point of intersection of the axes. Only a single ... moves the line of nodes around the external axis z, the second rotates around the line of nodes and the third one is an intrinsic rotationaround an axisfixed in the body that moves. These rotations are called Precession , Nutation , and rotation intrinsic rotation . Axis angle Main Axis angle Image Euler AxisAngle.png thumb right 150px A rotation represented by an Euler axis and angle. A second way of generalising the two dimensional angle of rotation is to specify an angle with the axis about ... the angle with this unit vector, called the rotation vector. Usually the angle and axis ... vector form of the axis angle rotation by the exponential map over the quaternions, math ... sub 1 sub and sub 2 sub is zero, one plane is fixed and the rotation is simple. If both sub 1 sub ... rotating a body clockwise about a point keeping the axes fixed is equivalent to rotating the axes counterclockwise about the same point while the body is kept fixed. Two dimensions Main U 1 Image Rotation4.svg right thumb A plane rotationaround a point followed by another rotationaround a different point results in a total motion which is either a rotation as in this picture , or a translation ... more details
Image Circle and its center.svg thumb right A circle. A complete rotation about the center point is equal to 1 turn geometry turn , 360 degree angle , or 2 pi radian s. In mathematics , the angle of rotation is a measurement of the amount, the angle , that a shape figure is rotation rotated about a fixed point mathematics fixed point , often the center geometry center of a circle . For example, the carts on a Ferris wheel move along a circle around the center point of that circle. If a cart moves around the wheel once, the angle of rotation is 360 degrees. If the cart was stuck halfway, at the top of the wheel, at that point its angle of rotation was only 180 degrees. Angles are commonly measured in degree angle degree s, radian s and turn geometry turns .... See also Hinge Plane of rotation Rotational symmetry Category Angle Geometry stub et P rdenurk ... more details
angle about a single fixedaxis of rotation see Euler s rotation theorem , and hence it can be simply ... the axis Image Rotation decomposition.png thumb A rotation R aroundaxis u can be decomposed ... to the rotationaxis must satisfy math R textbf u textbf u math since the rotation of math textbf u math around the rotationaxis must result in math textbf u math . The equation above may be solved ... math corresponds to a 30 rotationaround the x axis in three dimensional space. li li The 3 3 rotation ... corresponds to a rotation of approximately 74 around the axis sup 1 sup sub 3 sub , sup 2 sup sub ... sin , is a rotation by angle leaving axis u fixed. A direction in n 1 dimensional space ... build an n n rotation matrix by starting with a 2 2 matrix, aiming its fixedaxis on S sup 2 sup the ordinary ..., x , y , z , then we produce a 90 rotationaround the x axis for 1,0,0 , around the y axis for 0,1,0 ... as x goes to infinity, x ,0,0 does approach a 180 rotationaround the x axis, and similarly for other ... for a rotationaroundaxis u by angle . We also note that this mapping of skew symmetric matrices ... bmatrix . math This is our third version of this matrix, here as a rotationaround non unit axis ... is initially aligned with the x axis. In two dimensions every rotation matrix has the following ... axis to the right and the y axis up, the rotation R is counterclockwise. If a left handed Cartesian ..., would rotate toward the y axis a vector aligned with the x axis. This is similar to the rotation ... phi cos theta & cos phi cos theta end bmatrix math Conversion from and to axis angle Every rotation in three dimensions is defined by its axis &mdash a direction that is left fixed by the rotation &mdash and its angle &mdash the amount of rotation about that axis Euler rotation theorem . There are several methods to compute an axis and an angle from a rotation matrix see also axis angle . Here ... . Determining the angle To find the angle of a rotation, once the axis of the rotation is known ... more details
, the rotation period is in general not fixed, even in the absence of gravity gravitational or tidal force tidal forces. This is because, although the rotationaxis is fixed in space by the conservation of angular momentum , it is not necessarily fixed in the body of the object itself. As a result of this, the moment of inertia of the object around the rotationaxis can vary, and hence the rate of rotation can vary because the product of the moment of inertia and the rate of rotation is equal to the angular momentum, which is fixed . Hyperion moon Hyperion , a satellite of Saturn , exhibits this behaviour, and its rotation period is described as Chaos theory chaotic . Earth Earth s rotation ... Earth s rotation period relative to the fixed star s, called its stellar day by the International Earth Rotation and Reference Systems Service IERS , is nowrap 86164.098 903 691 seconds of mean solar ...The rotation period of an astronomy astronomical astronomical object object is the time that it takes to complete one revolution around its axis of rotation relative to the background stars. It differs from the planet s synodic day solar day , which includes an extra fractional rotation needed to accommodate the portion of the planet s orbital period during one day. Measuring rotation For solid objects, such as rocky planets and asteroids , the rotation period is a single value. For gaseous fluid bodies, such as star s and gas giant s, the period of rotation varies from the equator to the poles due to a phenomenon called differential rotation . Typically, the stated rotation period for a gas giant Jupiter, Saturn, Uranus, Neptune is its internal rotation period, as determined from the rotation ... 105 1982 359 361. ref Earth s rotation period relative to the precession astronomy precessing ... in SI seconds. Rotation period of selected objects class wikitable Celestial Objects colspan 2 Rotation ... table1.html Rotation and pole position for the Sun and planets Rotation period in days is 360 ... more details
The screw axis helical axis or twist axis of an Entity object is a line that is simultaneously the axis of rotation and the line along which a translation geometry translation occurs. Chasles theorem shows that each Euclidean group Euclidean displacement in three dimensional space has a screw axis, and the displacement can be decomposed into a rotation about and a slide along this screw axis. ref Bottema ... screw axis becomes the velocity pole, or instantaneous center of rotation , also called ... The proof that a spatial displacement can be decomposed into a rotation and slide around and along ... also screw operation is the composition of a rotation by an angle about an axis called the screw axis with a translation by a distance d along this axis. A positive rotation direction usually means ... screw operation generate different groups. The combination of a rotation about an axis and a translation in a perpendicular direction is a rotation about a parallel axis. However, a screw operation ... displacement. Applicable for space group s is a rotation by 360 n about an axis, combined with a translation ... , and 6 sub 5 sub . A non discrete screw axis isometry group contains all combinations of a rotation ... be a 2 fold rotation about a perpendicularly intersecting axis, and hence a k fold helix of such axes ... in the direction of the Axis angle representation rotationaxis of A . Points on this line translate ... along the screw axis in order to ensure that C exists. Solve this equation for C using Rotation matrix ..., Springer 2010 ref Mechanics The motion of a rigid body may be the combination of rotation about an axis ... of the moving instantaneous axis of rotation IAR is known as the centroid , and is used in the description ... a combination of rotation about an axis and a translation parallel to that axis leaves a crystal ... ref Pl cker coordinates are used to locate a screw axis in cartesian space space , and consist of a pair of three dimensional vectors. The first vector identifies the direction of the axis, and the second ... more details
Miscibility immiscible liquids rotating around a vertical axis is an upward opening circular paraboloid ... or absence of absolute rotation relative to the fixed stars rotating water has a curved surface ... Other thinkers suggest that pure logic implies only relative rotation makes sense. For example, Bishop Berkeley and Ernst Mach among others suggested that it is relative rotation with respect to the fixed stars that matters, and rotation of the fixed stars relative to an object has the same effect as rotation of the object with respect to the fixed stars. ref name Ridley cite book page 146 url http ... fashion, if we did not know the Earth rotates about its axis, we could infer this rotation from ...In physics , the consideration of absolute rotationrotation independent of any external reference is a topic ... s. The question of whether absolute rotation is meaningful is independent of the issue of the existence of absolute time and space . Is it meaningful to talk about absolute rotation? For the concept of absolute rotation to be scientifically meaningful, it must be measurable. In other words, can one ... suggestion was that rotation of a sphere such as a planet could be detected from its shape or figure ... around you, Mach suggests that there is some physical law which would make it so you would feel ... are rotating. Newton s conclusion was that rotation is absolute. ref cite book title Einstein s Theory ... for an operational definition of what we actually mean by absolute rotation. ref name Cohen Rather than justifying a causal link between rotation and centrifugal effects, Newton s arguments may be viewed as defining absolute rotation by stating a procedure for its detection and measurement involving ... and rotating at an angular rate . Because of the rotation, the string tying the spheres together is under tension. Newton also proposed another experiment to measure one s rate of rotation ... in the string indicates rotation of the spheres, whether or not the observer thinks they are rotating ... more details
In mathematics rotation group may refer to Circle group , the rotation group in two dimensions Rotation group SO 3 , the rotation group in three dimensions Rotations in 4 dimensional Euclidean space , the group SO 4 Orthogonal group , the general rotation group A rotation group or proper symmetry group with fixed point Cyclic group , rotational symmetry group for an object with n fold symmetry in a plane of rotation Point groups in three dimensions Rotation groups Point groups in three dimensions that are rotation groups See also Rotation disambiguation Symmetry group disambiguation mathdab ... more details
s usually show differential rotation and examples in our solar system include the Sun , Jupiter and Saturn . History Around the year 1610, Galileo Galilei observed sunspots and calculated the rotation ... i , where i is the angle between the line of sight and the rotationaxis, permitting the study of the rotational ...Unreferenced date December 2009 Differential rotation is seen when different parts of a rotating object move with different angular velocity angular velocities rates of rotation at different latitudes ... at the poles and at the equator, in good agreement with modern values. The cause of differential rotation Because of the pre stellar accretion phase, and the conservation of angular momentum , rotation is induced. Differential rotation is caused by convection in stars. This is movement of mass, due ... angular velocity in stellar wind s. Differential rotation thus depends on temperature differences in adjacent regions. Measuring differential rotation There are many ways to measure and calculate differential rotation in stars to see if different latitudes have different angular velocities. The most ... measurements of solar p modes it is possible to deduce the differential rotation. The Sun has very ... can yield the rotation of the solar interior. This varies with both depth and especially latitude ... also plot 2. Solar differential rotation is also seen in magnetograms, images showing the strength and location of solar magnetic fields. Effects of differential rotation Gradients in angular rotation ... mechanisms in the outer envelopes. The interface between these two regions is where angular rotation ... differential rotation is one part of the mixing processes in stars, mixing the materials and the heat energy of the stars. Differential rotation affects stellar optical absorption line spectra through ... surface. Solar differential rotation causes shear at the so called tachocline. This is a region where rotation changes from differential in the convection zone to nearly solid body rotation in the interior ... more details
is an affine transformation with an orthogonal matrix that has a determinant of 1. A proper rotation is an ordinary rotation. In the wider sense, a proper rotation is a direct isometry , i.e., an element of E sup sup 3 it can also be the identity, a rotation with a translation along the axis, or a pure ...Unreferenced date January 2008 In 3D geometry , an improper rotation , also called rotoreflection or rotary reflection is, depending on context, a linear transformation or affine transformation which is the combination of a rotation about an axis and a reflection in a plane perpendicular to the axis. Equivalently it is the combination of a rotation and an inversion in a point on the axis. Therefore it is also called a rotoinversion or rotary inversion . In both cases the operations commute. Rotoreflection and rotoinversion are the same if they differ in angle of rotation by 180 , and the point of inversion is in the plane of reflection. An improper rotation of an object thus produces a rotation of its mirror image . The axis is called the rotation reflection axis . This is called an n fold improper rotation if the angle of rotation is 360 n . The notation S sub n sub S for Spiegel , German for mirror denotes the symmetry group generated by an n fold improper rotation not to be confused ... , i.e. rotation by an angle of rotation of 360 n with inversion. In the wider sense, an improper rotation is an indirect isometry , i.e., an element of E 3 E sup sup 3 see Euclidean group it can ... a determinant of 1. In the wider senses, the composition of two improper rotations is a proper rotation, and the product of an improper and a proper rotation is an improper rotation. When studying the symmetry of a physical system under an improper rotation e.g., if a system has a mirror symmetry ... symmetries Category Lie groups de Drehspiegelung fr Antirotation ja simple Improper rotation sv Oegentlig rotation ... more details
Solar rotation is able to vary with latitude because the Sun is composed of a gaseous Plasma physics plasma . The rate of rotation is observed to be fastest at the equator latitude 0 deg , and to decrease as latitude increases. The differential rotation rate is usually described by the equation math ... last Beck first J. title A comparison of differential rotation measurements journal Solar Physics volume ... ref Cite journal last1 Snodgrass first1 H. last2 Ulrich first2 R. title Rotation of Doppler features ... deg day 0.253 Sidereal rotation At the equator the solar rotation period is 24.47 days. This is called the sidereal rotation period, and should not be confused with the synodic rotation period of 26.24 days, which is the time for a fixed feature on the Sun to rotate to the same apparent position ... plus an extra amount due to the orbital motion of the Earth around the Sun. Note that astrophysical literature does not typically use the equatorial rotation period, but instead often uses the definition of a Carrington rotation a synodic rotation period of 27.2753 days or a sidereal period of 25.38 days . This chosen period roughly corresponds to rotation at a latitude of 26 deg, which is consistent ... is viewed from the north above the Earth s northern pole solar rotation is counterclockwise. Sunspots .... Using sunspots to measure rotation The rotation constants have been measured by measuring the motion ... into use that they were observed to turn with the Sun, and thus the period of the solar rotation could ... Narratio Narration on Spots Observed on the Sun and their Apparent Rotation with the Sun were by Johannes ... rotation. Christopher Scheiner Rosa Ursine sive solis , book 4, part 2, 1630 was the first to measure the equatorial rotation rate of the Sun and noticed that the rotation at higher latitudes is slower, so he can be considered the discoverer of solar differential rotation. Each measurement ... was perhaps the first to summarise the published solar rotation rates, and concluded that the differences ... more details
In combinatorics combinatorial mathematics , rotation systems encode embeddings of graph theory graphs onto orientability orientable surface s, by describing the circular ordering of a graph s edges around each vertex. A more formal definition of a rotation system involves pairs of permutations such a pair ... onto the surface. Every rotation scheme defines a unique 2 cell embedding of a connected ... rotation system having G as its underlying multigraph. This fundamental equivalence between rotation ... set of multigraphs was developed by Gross and Alpert. Rotation systems are related to, but not the same as, the rotation map s used by Reingold et al. 2002 to define the zig zag product of graphs. A rotation system specifies a circular ordering of the edges around each vertex, while a rotation map specifies a non circular permutation of the edges at each vertex. In addition, rotation systems can be defined for any graph, while as Reingold et al. define them rotation maps are restricted to regular graph s. Formal definition Formally, a rotation system is defined as a pair , where and are permutations acting on the same ground set B , is a fixed point free Involution mathematics ... Group action acts transitively on B . To derive a rotation system from a 2 cell embedding of a connected ... b be the other dart formed from the same edge as b this is clearly an involution with no fixed points ... on an orientable but not oriented surface, it generally corresponds to two rotation systems, one for each of the two orientations of the surface. These two rotation systems have the same involution , but the permutation for one rotation system is the inverse of the corresponding permutation for the other rotation system. Recovering the embedding from the rotation system To recover a multigraph from a rotation system, we form a vertex for each orbit of , and an edge for each orbit of ... two. If a rotation system is derived from a 2 cell embedding of a connected multigraph G , the graph ... more details
unreferenced date May 2011 merge tidal locking date November 2011 Image Synchronous rotation.svg thumb Due to synchronous rotation of their moon, the inhabitants of the central body will never be able to see its side marked with green. In astronomy , synchronous rotation is a planetology planetological term describing a body orbit ing another, where the orbiting body takes as long to rotate on its axis of rotation axis as it does to make one orbit and therefore always keeps the same hemisphere pointed at the body it is orbiting. Another way of describing it is that from the surface of the satellite, the main planet appears to be locked in place in the sky as it slowly rotates. The Moon is in synchronous rotation about the Earth , and Iapetus moon Iapetus is in synchronous rotation about Saturn . See also Tidal locking Tidal acceleration Rotation Synchronous orbit Orbital resonance Category Planetary science astronomy stub af Sinkroniese omwenteling als Gebundene Rotation ar bg ca Rotaci s ncrona cs V zan rotace da Bunden rotation de Gebundene Rotation es Rotaci n s ncrona eo Ligita rotacio fr Rotation synchrone ko hr Sinkrona rotacija it Rotazione sincrona he nl Synchronisatiehoogte ja no Bundet rotasjon nn Bunden rotasjon nds Bunnen Rotatschoon pl Obr t synchroniczny pt Rota o sincronizada ru sk Viazan rot cia sl So asno vrtenje sv Bunden rotation vi Qu o quay ng b zh ... more details
along a conic surface around the axis of rotation. A neutron star is a highly dense remnant ... caused by rapid rotation. Stellar rotation is the angular motion of a star about its axis. The rate of rotation can be measured from the spectrum of the star, or by timing the movements of active features on the surface. The rotation of a star produces an equatorial bulge due to centrifugal force . As stars are not solid bodies, they can also undergo differential rotation . Thus the equator of the star ... equilibrium. The effect can be more complex in cases where the axis of rotation is not perpendicular ... of rotation within a star may have a significant role in the generation of a stellar magnetic ... field of the star interacts with the wind, which applies a drag to the stellar rotation. As a result ... s rate of rotation. Measurement Unless a star is being observed from the direction of its pole ... author Shajn, G. Struve, O. title On the rotation of the stars journal Monthly Notices of the Royal ... of microturbulence to be distinguished from rotation. ref cite journal last Gould first Andrew title Measuring the Rotation Speed of Giant Stars from Gravitational Microlensing journal Astrophysical Journal ... can be tracked to estimate the rotation rate. However, such features can form at locations other ... rotation of a star can produce varying measurements. Stellar magnetic activity is often associated with rapid rotation, so this technique can be used for measurement of such stars. ref cite journal author Soon, W. Frick, P. Baliunas, S. title On the rotation of the stars journal The Astrophysical ... the rotation rate of a star, as the magnetic fields modify the flow of gases in the star. ref cite ... differential rotation on AB Doradus journal Monthly Notices of the Royal Astronomical Society year ... to a more spherical shape. The rotation also gives rise to gravity darkening at the equator, as described ... 3 km s. This corresponds to a rotation period of 15.9 hours, which is 86 of the velocity ... more details
Unreferenced date January 2008 In physics , Wick rotation , named after Gian Carlo Wick , is a method of finding a solution to a mathematical problem in Minkowski space from a solution to a related problem in Euclidean space by means of a transformation that substitutes an imaginary number variable for a real number variable. This transformation is also used to find solutions to problems in quantum mechanics and other areas. Overview It is motivated by the observation that the Minkowski metric tensor metric with &minus 1, 1, 1, 1 convention for the metric tensor math ds 2 dt 2 dx 2 dy 2 dz 2 math and the four dimensional Euclidean metric math ds 2 d tau 2 dx 2 dy 2 dz 2 math are equivalent if one ... Euclidean when t is restricted to the imaginary number imaginary axis , and vice versa. Taking ... problem. Statistical and quantum mechanics Wick rotation connects statistical mechanics to quantum ... math sum j Q j e E j it hbar . math Statics and dynamics Wick rotation relates statics problems in math ... for one dimension of time. A simple example where math n 2 math is a hanging spring with fixed endpoints ... problem up to a factor of math i math from the statics problem by Wick rotation, replacing ... equation and the heat equation are also related by Wick rotation. However, there is a slight ... field theories satisfy Schwinger function reflection positivity . It is called a rotation because ... imaginary time in his famous book A Brief History of Time , he was referring to Wick rotation. citation needed date November 2010 Wick rotation also relates a QFT at a finite inverse temperature to a statistical ... coordinate being periodic with period . Note, however, that the Wick rotation cannot be viewed as a rotation ... by the inner product , as in this case the rotation would cancel out and have no effect at all. See ... particle DEFAULTSORT Wick Rotation Category Quantum field theory Category Statistical mechanics de Wick Rotation ja pt Rota o de Wick ru zh ... more details
. The yaw rate anyway can still be measured with accelerometers in the vertical axis. Any device ... forces are available in the main article. Relationship with other rotation systems These rotations ... formulas . Performing a rotation in an intrinsic reference frame is equivalent to right multiply its ... of the rotation. History The first aircraft to demonstrate active control about all three axes was the Wright ... more details
refimprove date October 2010 Rotation of ammunition is a term used with reference to gun s. Projectile s intended for R.M.L. rifled muzzle loading gun rifled muzzle loading guns were at first fitted with a number of gunmetal gun metal studs arranged around them in a spiral manner corresponding to the twist of rifling . This was defective, as it allowed, as in the old smooth bore guns, the powder gas to escape by the clearance called windage between the projectile and the bore, with a consequent loss of efficiency it also quickly eroded the bore of the larger guns. Later the rotation was effected by a cupped copper disc called a gas check attached to the base end of the projectile. The powder gas pressure expanded the rim of the gas check into the rifling grooves and prevented the escape of gas it also firmly fixed the gas check to the projectile, thus causing it to rotate. A more regular and efficient action of the powder gas was thus ensured, with a corresponding greater range and an improvement in accuracy. With the earlier Armstrong R.B.L. or rifled breech loading guns rifled breech loading guns the projectiles were coated with lead the late Lord Armstrong s system , the lead being forced through the rifling grooves by the pressure of the exploded powder gas. The lead coating is, however, too soft with the higher velocities of modern B.L. guns. Vavasseur devised the plan of fitting by hydraulic pressure a copper driving band into a groove cut around the body of the projectile. This is now universal. It not only fulfills the purpose of rotating the projectile, but renders possible the use of large explosive charge charges of slow burning explosive . The copper band, on being forced through the gun, gives rise to considerable friction resistance , which allows the propelling charge to burn properly and thus to exert its enormous force on the projectile. The laws which govern projectile designs are not well defined. Certain formulae are used which give the thickness ... more details
This article is about the rotation number , which is sometimes called the map winding number or simply winding number . There is another meaning for winding number , which appears in complex analysis . In mathematics , the rotation number is an invariant of homeomorphism s of the circle . It was first ... number rationality of the rotation number. Definition Suppose that f S sup 1 sup S sup 1 ... math for every real number x and every integer m . The rotation number of f is defined in terms of the iterated ... is unique modulo integers, therefore the rotation number is a well defined element of R Z . Intuitively, it measures the average rotation angle along the orbit dynamics orbits of f . Example If f is a rotation by , so that math F x x theta, math then its rotation number is cf Irrational rotation . Properties The rotation number is invariant under topological conjugacy , and even topological semiconjugacy ... map h of the circle into itself not necessarily homeomorphic then f and g have the same rotation ... of the circle. There are two distinct possibilities. The rotation number of f is a rational number ... of the points on each such orbit coincides with the order of the points for a rotation by p ... and backward directions may be different. The rotation number of f is an irrational number ... rotation by the angle &theta and all orbits are dense set dense . Denjoy proved that this possibility ... and backward direction converge to C . In this case, f is semiconjugate to the irrational rotation by &theta ... . Rotation number is continuous when viewed as a map from the group of homeomorphisms with math C ... du cercle des rotations , Publ. Math. IHES, 49 1979 pp. 5 234 Scholarpedia title Rotation theory urlname Rotation theory curator Micha Misiurewicz Sebastian van Strien, http www.maths.warwick.ac.uk strien MA424 HTMLversion node6.html Rotation Numbers and Poincar s Theorem 2001 Category Fixed points mathematics Category Dynamical systems fr Nombre de rotation nl Rotatiegetal pl Liczba obrotu ... more details
Encyclopedia
top
