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Discovery Of Precession
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called ''nutation''. In physics, there are two types of precession: torque-free and torque-induced. In astronomy, ''precession'' refers to any of several slow changes in an astronomical body's rotational or orbital parameters. An important example is the steady change in the orientation of the axis of rotation of the Earth, known as the precession of the equinoxes. Torque-free Torque-free precession implies that no external moment (torque) is applied to the body. In torque-free precession, the angular momentum is a constant, but the angular velocit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gyroscope Precession
A gyroscope (from Ancient Greek γῦρος ''gŷros'', "round" and σκοπέω ''skopéō'', "to look") is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rotation (spin axis) is free to assume any orientation by itself. When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, according to the conservation of angular momentum. Gyroscopes based on other operating principles also exist, such as the microchip-packaged MEMS gyroscopes found in electronic devices (sometimes called gyrometers), solid-state ring lasers, fibre optic gyroscopes, and the extremely sensitive quantum gyroscope. Applications of gyroscopes include inertial navigation systems, such as in the Hubble Space Telescope, or inside the steel hull of a submerged submarine. Due to their precision, gyroscopes are also used in gyrotheodolites to maintain direction in tunnel mining. Gyroscopes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Component
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a '' directed line segment'', or graphically as an arrow connecting an ''initial point'' ''A'' with a ''terminal point'' ''B'', and denoted by \overrightarrow . A vector is what is needed to "carry" the point ''A'' to the point ''B''; the Latin word ''vector'' means "carrier". It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from ''A'' to ''B''. Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Direction (geometry, Geography)
Body relative directions (also known as egocentric coordinates) are geometrical orientations relative to a body such as a human person's. The most common ones are: left and right; forward(s) and backward(s); up and down. They form three pairs of orthogonal axes. Traditions and conventions Since definitions of left and right based on the geometry of the natural environment are unwieldy, in practice, the meaning of relative direction words is conveyed through tradition, acculturation, education, and direct reference. One common definition of up and down uses gravity and the planet Earth as a frame of reference. Since there is a very noticeable force of gravity acting between the Earth and any other nearby object, down is defined as that direction which an object moves in reference to the Earth when the object is allowed to fall freely. Up is then defined as the opposite direction of down. Another common definition uses a human body, standing upright, as a frame of reference. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right Angle
In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. The term is a calque of Latin ''angulus rectus''; here ''rectus'' means "upright", referring to the vertical perpendicular to a horizontal base line. Closely related and important geometrical concepts are perpendicular lines, meaning lines that form right angles at their point of intersection, and orthogonality, which is the property of forming right angles, usually applied to vectors. The presence of a right angle in a triangle is the defining factor for right triangles, making the right angle basic to trigonometry. Etymology The meaning of ''right'' in ''right angle'' possibly refers to the Latin adjective ''rectus'' 'erect, straight, upright, perpendicular'. A Greek equivalent is ''orthos'' 'straight; perpendicular' (see orthogon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnitude (mathematics)
In mathematics, the magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects of the same kind. More formally, an object's magnitude is the displayed result of an ordering (or ranking)—of the class of objects to which it belongs. In physics, magnitude can be defined as quantity or distance. History The Greeks distinguished between several types of magnitude, including: *Positive fractions *Line segments (ordered by length) * Plane figures (ordered by area) * Solids (ordered by volume) * Angles (ordered by angular magnitude) They proved that the first two could not be the same, or even isomorphic systems of magnitude. They did not consider negative magnitudes to be meaningful, and ''magnitude'' is still primarily used in contexts in which zero is either the smallest size or less than all possible sizes. Numbers The magnitude of any number x is usually called its ''absolute value'' or ''modulus'', de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speed
In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ... of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; the instantaneous speed is the limit (mathematics), limit of the average speed as the duration of the time interval approaches zero. Speed is #Difference between speed and velocity, not the same as velocity. Speed has the dimensional analysis, dimensions of distance divided by time. The International System of Units, SI unit of speed is the metre per s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spinning Top
A spinning top, or simply a top, is a toy with a squat body and a sharp point at the bottom, designed to be spun on its vertical axis, balancing on the tip due to the gyroscopic effect. Once set in motion, a top will usually wobble for a few seconds, spin upright for a while, then start to wobble again with increasing amplitude as it loses energy, and finally tip over and roll on its side. Tops exist in many variations and materials, chiefly wood, metal, and plastic, often with a metal tip. They may be set in motion by twirling a handle with the fingers, by pulling a rope coiled around the body, or by means of a built-in auger (spiral plunger). Such toys have been used since antiquity in solitary or competitive games, where each player tries to keep one's top spinning for as long as possible, or achieve some other goal. Some tops have faceted bodies with symbols or inscriptions, and are used like dice to inject randomness into games, or for divination and ritual purposes. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cone (geometry)
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex. Depending on the author, the base may be restricted to be a circle, any one-dimensional quadratic form in the plane, any closed one-dimensional figure, or any of the above plus all the enclosed points. If the enclosed points are included in the base, the cone is a solid object; otherwise it is a two-dimensional object in three-dimensional space. In the case of a solid object, the boundary formed by these lines or partial lines is called the ''lateral surface''; if the lateral surface is unbounded, it is a conical surface. In the case of line segments, the cone does not extend beyond the base, while in the case of half- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gyroscope
A gyroscope (from Ancient Greek γῦρος ''gŷros'', "round" and σκοπέω ''skopéō'', "to look") is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rotation (spin axis) is free to assume any orientation by itself. When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, according to the conservation of angular momentum. Gyroscopes based on other operating principles also exist, such as the microchip-packaged MEMS gyroscopes found in electronic devices (sometimes called gyrometers), solid-state ring lasers, fibre optic gyroscopes, and the extremely sensitive quantum gyroscope. Applications of gyroscopes include inertial navigation systems, such as in the Hubble Space Telescope, or inside the steel hull of a submerged submarine. Due to their precision, gyroscopes are also used in gyrotheodolites to maintain direction in tunnel mining. Gyroscope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axis Of Rotation
Rotation around a fixed axis is a special case of rotational motion. The fixed- axis hypothesis excludes the possibility of an axis changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will appear. This article assumes that the rotation is also stable, such that no torque is required to keep it going. The kinematics and dynamics of rotation around a fixed axis of a rigid body are mathematically much simpler than those for 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 energy of the object, and for the forces on the parts of the object, are also simpler for rotation around a fixed axis, than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross Product
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is denoted by the symbol \times. Given two linearly independent vectors and , the cross product, (read "a cross b"), is a vector that is perpendicular to both and , and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with the dot product (projection product). If two vectors have the same direction or have the exact opposite direction from each other (that is, they are ''not'' linearly independent), or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotation Representation (mathematics)
In geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at a given instant is described with the same tools, as it is defined as an imaginary rotation from a reference placement in space, rather than an actually observed rotation from a previous placement in space. According to Euler's rotation theorem the rotation of a rigid body (or three-dimensional coordinate system with the fixed origin) is described by a single rotation about some axis. Such a rotation may be uniquely described by a minimum of three real parameters. However, for various reasons, there are several ways to represent it. Many of these representations use more than the necessary minimum of three parameters, although each of them still has only three degr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
