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Pop (physics)
In physics, the fourth, fifth and sixth derivatives of position are defined as derivatives of the position vector with respect to time – with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively. The higher-order derivatives are less common than the first three; thus their names are not as standardized, though the concept of a minimum snap trajectory has been used in robotics. The fourth derivative is referred to as snap, leading the fifth and sixth derivatives to be "sometimes somewhat facetiously" called crackle and pop, named after the Rice Krispies mascots of the same name. The fourth derivative is also called jounce. (snap/jounce) Snap, or jounce, is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Derivatives Of Position
Time is the continuous progression of existence that occurs in an apparently irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequence events, to compare the duration of events (or the intervals between them), and to quantify rates of change of quantities in material reality or in the conscious experience. Time is often referred to as a fourth dimension, along with three spatial dimensions. Time is one of the seven fundamental physical quantities in both the International System of Units (SI) and International System of Quantities. The SI base unit of time is the second, which is defined by measuring the electronic transition frequency of caesium atoms. General relativity is the primary framework for understanding how spacetime works. Through advances in both theoretical and experimental investigations of spacetime, it has been shown that time can be distorted and dilated, particularl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Civil Engineering
Civil engineering is a regulation and licensure in engineering, professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewage systems, pipelines, structural element, structural components of buildings, and railways. Civil engineering is traditionally broken into a number of sub-disciplines. It is considered the second-oldest engineering discipline after military engineering, and it is defined to distinguish non-military engineering from military engineering. Civil engineering can take place in the public sector from municipal public works departments through to federal government agencies, and in the private sector from locally based firms to Fortune Global 500, ''Fortune'' Global 500 companies. History Civil engineering as a discipline Civil engineering is the application of physical and scientific principles for solv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinematic Properties
In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion such as linked machine parts are also described as kinematics. Kinematics is concerned with systems of specification of objects' positions and velocities and mathematical transformations between such systems. These systems may be rectangular like Cartesian coordinate system, cartesian, Curvilinear coordinates like polar coordinates or other systems. The object trajectories may be specified with respect to other objects which may themselve be in motion relative to a standard reference. Rotating systems may also be used. Numerous practical problems in kinematics involve constraints, such as mechanical linkages, ropes, or rolling disks. Overview Kinematics is a subfield of physics and mathematics, developed in classical mechanics, that describes the motion of points, Physical object, bodies (objects), and systems of bodies (group ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acceleration
In mechanics, acceleration is the Rate (mathematics), rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are Euclidean vector, vector quantities (in that they have Magnitude (mathematics), magnitude and Direction (geometry), direction). The orientation of an object's acceleration is given by the orientation of the ''net'' force acting on that object. The magnitude of an object's acceleration, as described by Newton's second law, is the combined effect of two causes: * the net balance of all external forces acting onto that object — magnitude is Direct proportionality, directly proportional to this net resulting force; * that object's mass, depending on the materials out of which it is made — magnitude is Inverse proportionality, inversely proportional to the object's mass. The International System of Units, SI unit for acceleration is metre per second squared (, \ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Riverside
The University of California, Riverside (UCR or UC Riverside) is a public university, public Land-grant university, land-grant research university in Riverside, California, United States. It is one of the ten campuses of the University of California system. The main campus sits on in a suburban district of Riverside with a branch campus of in Palm Desert, California, Palm Desert. In 1907, the predecessor to UCR was founded as the UC Citrus Experiment Station, which conducted research in biological pest control and the use of plant hormone, growth regulators. UCR's undergraduate UCR College of Humanities, Arts, and Social Sciences, College of Letters and Science opened in 1954. The Regents of the University of California declared UCR a general campus of the system in 1959, and graduate students were admitted in 1961. To accommodate an enrollment of 21,000 students by 2015, more than $730 million has been invested in new construction projects since 1999. UCR plans to have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical And Quantum Gravity
''Classical and Quantum Gravity'' is a peer-reviewed journal that covers all aspects of gravitational physics and the theory of spacetime. The editor-in-chief is Susan Scott at The Australian National University. The journal's 2023 impact factor is 3.6 according to Journal Citation Reports. As of October 2015, the journal publishes letters in addition to regular articles. Scope The journal's scope includes: * Classical general relativity * Applications of relativity * Experimental gravitation * Cosmology and the early universe * Quantum gravity * Supergravity, superstrings and supersymmetry * Mathematical physics relevant to gravitation ''Classical and Quantum Gravity'' also supports the field of gravitational physics through sponsorship of the British Gravity Meeting. ''CQG+'' Until the end of 2023, the journal used to have a companion blog website, called "CQG+", that highlighted high-quality papers published in the journal in order to raise the visibility of those p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SI Unit
The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of units of measurement, system of measurement. It is the only system of measurement with official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce. The SI system is coordinated by the International Bureau of Weights and Measures, which is abbreviated BIPM from . The SI comprises a coherence (units of measurement), coherent system of unit of measurement, units of measurement starting with seven SI base unit, base units, which are the second (symbol s, the unit of time), metre (m, length), kilogram (kg, mass), ampere (A, electric current), kelvin (K, thermodynamic temperature), mole (unit), mole (mol, amount of substance), and candela (cd, luminous intensity). The system can accommodate coherent units for an unlimited number of additional quantiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Displacement Vector
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation that maps the initial position to the final position. Displacement is the shift in location when an object in motion changes from one position to another. For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude is the average speed (a scalar quantity). Formulation A displacement may be formulated as a '' relative position'' (resulting from the motion), that is, as the final position of a point relative to its initial position . The corresponding displacement vector can be defined as the differen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clothoid
An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). This curve is also referred to as a clothoid or Cornu spiral.Levien, Raph"The Euler spiral: a mathematical history."Rapp. tech (2008). The behavior of Fresnel integrals can be illustrated by an Euler spiral, a connection first made by Marie Alfred Cornu in 1874. Euler's spiral is a type of superspiral that has the property of a monotonic curvature function. The Euler spiral has applications to diffraction computations. They are also widely used in railway and highway engineering to design transition curves between straight and curved sections of railways or roads. A similar application is also found in photonic integrated circuits. The principle of linear variation of the curvature of the transition curve between a tangent and a circular curve defines the geometry of the Euler spiral: *Its curvature begins with zero at t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radial Acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the orientation of the ''net'' force acting on that object. The magnitude of an object's acceleration, as described by Newton's second law, is the combined effect of two causes: * the net balance of all external forces acting onto that object — magnitude is directly proportional to this net resulting force; * that object's mass, depending on the materials out of which it is made — magnitude is inversely proportional to the object's mass. The SI unit for acceleration is metre per second squared (, \mathrm). For example, when a vehicle starts from a standstill (zero velocity, in an inertial frame of reference) and travels in a straight line at increasing spee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radius Of Curvature
In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. Definition In the case of a space curve, the radius of curvature is the length of the curvature vector. In the case of a plane curve, then is the absolute value of : R \equiv \left, \frac \ = \frac, where is the arc length from a fixed point on the curve, is the tangential angle and is the curvature. Formula In two dimensions If the curve is given in Cartesian coordinates as , i.e., as the graph of a function, then the radius of curvature is (assuming the curve is differentiable up to order 2) R =\left, \frac \\,, where y' = \frac\,, y'' = \frac, and denotes the absolute value of . If the curve is given parametrically by functions and , then the radiu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Railway Track
Railway track ( and UIC terminology) or railroad track (), also known as permanent way () or "P way" ( and Indian English), is the structure on a railway or railroad consisting of the rails, fasteners, sleepers ( railroad ties in American English) and ballast (or slab track), plus the underlying subgrade. It enables trains to move by providing a dependable, low-friction surface on which steel wheels can roll. Early tracks were constructed with wooden or cast-iron rails, and wooden or stone sleepers. Since the 1870s, rails have almost universally been made from steel. Historical development The first railway in Britain was the Wollaton wagonway, built in 1603 between Wollaton and Strelley in Nottinghamshire. It used wooden rails and was the first of about 50 wooden-railed tramways built over the subsequent 164 years. These early wooden tramways typically used rails of oak or beech, attached to wooden sleepers with iron or wooden nails. Gravel or small stones were pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
