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Mechanical Engineering经典概率密度经典概率密度是概率密度函数，表示在经典机械系统中在某个位置附近发现受势能影响的粒子的可能性。这些概率密度有助于深入了解对应原理并在所研究的量子系统与经典极限之间建立联系。
The classical probability density is the probability density function that represents the likelihood of finding a particle in the vicinity of a certain location subject to a potential energy in a classical mechanical system. These probability densities are helpful in gaining insight into the correspondence principle and making connections between the quantum system under study and the classical limit.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在经典物理学和狭义相对论中，惯性参考系（也称为惯性空间或伽利略参考系）是物体表现出惯性的参考系：它们相对于参考系保持静止或匀速运动，直到受到外力作用。在这样的框架中，无需校正加速度即可观察自然法则。所有零加速度的参考系都处于相对于彼此恒定直线运动（直线运动）的状态。在这样的框架中，作用在其上的净力为零的物体被认为以恒定速度移动，或者等效地，牛顿第一运动定律成立。这种框架被称为惯性框架。一些物理学家，比如艾萨克·牛顿，最初认为其中一个框架是绝对的——即以恒星近似的框架。
In classical physics and special relativity, an inertial frame of reference (also called an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative to the frame until acted upon by external forces. In such a frame, the laws of nature can be observed without the need to correct for acceleration. All frames of reference with zero acceleration are in a state of constant rectilinear motion (straight-line motion) with respect to one another. In such a frame, an object with zero net force acting on it, is perceived to move with a constant velocity, or, equivalently, Newton's first law of motion holds. Such frames are known as inertial. Some physicists, like Isaac Newton, originally thought that one of these frames was absolute — the one approximated by the fixed stars.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 惯性是运动中的物体保持运动状态和静止的物体保持静止状态的自然趋势，除非有力导致其速度改变。它是经典物理学的基本原理之一，由艾萨克·牛顿在他的第一运动定律（也称为惯性原理）中进行了描述。它是质量的主要表现之一，是物理系统的核心定量特性之一。牛顿写道：第一定律。每个物体都保持静止状态，或者沿直线匀速运动，除非它受到施加在其上的力的作用而被迫改变该状态。牛顿在 1687 年的著作《自然哲学数学原理》中将惯性定义为一种属性：定义 III。
Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes its velocity to change. It is one of the fundamental principles in classical physics, and is described by Isaac Newton in his first law of motion (also known as The Principle of Inertia). It is one of the primary manifestations of mass, one of the core quantitative properties of physical systems. Newton writes: LAW I. Every object perseveres in its state of rest, or of uniform motion in a right line, except insofar as it is compelled to change that state by forces impressed thereon. In his 1687 work Philosophiæ Naturalis Principia Mathematica, Newton defined inertia as a property: DEFINITION III.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 加加速度（也称为摇动）是物体加速度随时间的变化率。它是一个矢量（具有大小和方向）。加加速度最常用符号 j 表示，并以 m/s3（SI 单位）或标准重力每秒 (g0/s) 表示。
Jerk (also known as jolt) is the rate of change of an object's acceleration over time. It is a vector quantity (having both magnitude and direction). Jerk is most commonly denoted by the symbol j and expressed in m/s3 (SI units) or standard gravities per second(g0/s).
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 与弹性碰撞相反，非弹性碰撞是由于内摩擦力的作用而动能不守恒的碰撞。在宏观物体的碰撞中，一些动能转化为原子的振动能，引起加热效应，物体发生变形。气体或液体的分子很少经历完美的弹性碰撞，因为每次碰撞时，分子的平移运动与其内部自由度之间都会交换动能。在任何一个瞬间，一半的碰撞在不同程度上是非弹性的（碰撞后碰撞后比碰撞前拥有更少的动能），一半可以被描述为“超弹性”（碰撞后碰撞后比碰撞前拥有更多的动能）。对整个样品进行平均，分子碰撞是有弹性的。
An inelastic collision, in contrast to an elastic collision, is a collision in which kinetic energy is not conserved due to the action of internal friction. In collisions of macroscopic bodies, some kinetic energy is turned into vibrational energy of the atoms, causing a heating effect, and the bodies are deformed. The molecules of a gas or liquid rarely experience perfectly elastic collisions because kinetic energy is exchanged between the molecules' translational motion and their internal degrees of freedom with each collision. At any one instant, half the collisions are – to a varying extent – inelastic (the pair possesses less kinetic energy after the collision than before), and half could be described as “super-elastic” (possessing more kinetic energy after the collision than before). Averaged across an entire sample, molecular collisions are elastic.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在经典力学中，冲量（用 J 或 Imp 表示）是物体动量的变化。它最常用于描述在短时间内作用的力，特别是在撞击和碰撞的情况下，它因此而得名。冲量是一个矢量，这意味着它既有描述动量变化量的大小，也有描述动量变化方向的方向。对于短时间作用的力，冲量通常被理想化，以便将力产生的动量变化建模为瞬时发生。这种变化是阶跃变化，在物理上是不可能的。然而，这是计算理想碰撞效果的有用模型（例如在视频游戏物理引擎中）。
In classical mechanics, impulse (symbolized by J or Imp) is the change in momentum of an object. It is most often used to describe forces which act over short time periods, specifically in the case of impacts and collisions, for which it gets its namesake. Impulse is a vector quantity, meaning it has both a magnitude, which describes the amount by which the momentum changed, and a direction, which describes the direction in which the momentum changed. For a force acting over a short time, the impulse is often idealized so that the change in momentum produced by the force is modelled as happening instantaneously. This sort of change is a step change, and is not physically possible. However, this is a useful model for computing the effects of ideal collisions (such as in videogame physics engines).
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 喷射力是某些机器（尤其是飞机）的排气，根据牛顿第三定律将物体本身推向相反的方向。对喷气力的理解是无人机、卫星、火箭、飞机和其他机载机器的发射所固有的。喷射力始于某种推进系统；对于火箭来说，这通常是一些从底部排出可燃气体的系统。该斥力系统如此迅速地将这些气体分子沿与预期运动相反的方向推出，以至于与气体分子移动方向成 180° 作用的相反力（因此，沿预期的运动方向）将火箭向上推。一个常见的错误假设是火箭通过推离地面而升起。
Jet force is the exhaust from some machine, especially aircraft, propelling the object itself in the opposite direction as per Newton's third law. An understanding of jet force is intrinsic to the launching of drones, satellites, rockets, airplanes and other airborne machines. Jet force begins with some propulsion system; in the case of a rocket, this is usually some system that kicks out combustible gases from the bottom. This repulsion system pushes out these gas molecules in the direction opposite the intended motion so rapidly that the opposite force, acting 180° away from the direction the gas molecules are moving, (as such, in the intended direction of movement) pushes the rocket up. A common wrong assumption is that the rocket elevates by pushing off the ground.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 初始稳定性或初级稳定性是船对施加在其两侧的垂直力之间的差异的微小变化的抵抗力。初始稳性和次稳性的研究是应用于小型船舶的船舶建筑学的一部分（与大型船舶的船舶稳定性研究不同）。
Initial stability or primary stability is the resistance of a boat to small changes in the difference between the vertical forces applied on its two sides. The study of initial stability and secondary stability are part of naval architecture as applied to small watercraft (as distinct from the study of ship stability concerning large ships).
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在物理学中，冲击参数 b 定义为弹丸路径与弹丸接近的物体所产生的势场 U(r) 中心之间的垂直距离（见图）。它经常在核物理学（参见卢瑟福散射）和经典力学中被提及。
In physics, the impact parameter b is defined as the perpendicular distance between the path of a projectile and the center of a potential field U(r) created by an object that the projectile is approaching (see diagram). It is often referred to in nuclear physics (see Rutherford scattering) and in classical mechanics.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 当电势施加在金属表面与半导体材料或聚电解质表面之间的边界上时，就会发生约翰森-拉贝克效应。在这些条件下，会出现吸引力，其大小取决于电压和所涉及的具体材料。吸引力比库仑吸引力产生的力大得多。该效应以丹麦工程师 F. A. Johnsen 和 K. Rahbek 的名字命名，他们是第一个详细研究该效应的人。
The Johnsen–Rahbek effect occurs when an electric potential is applied across the boundary between a metallic surface and the surface of a semiconducting material or a polyelectrolyte. Under these conditions an attractive force appears, whose magnitude depends on the voltage and the specific materials involved. The attractive force is much larger than would be produced by Coulombic attraction. The effect is named after Danish engineers F. A. Johnsen and K. Rahbek, the first to investigate the effect at length.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 进行平面运动的物体的瞬时旋转中心（也称为瞬时速度中心、瞬时中心或平面位移极点）是在特定时刻速度为零的点。此时，物体中其他点的速度矢量围绕该旋转中心产生一个圆形位移场，这与纯旋转产生的位移场相同。物体的平面运动通常用在二维平面上运动的平面图形来描述。瞬时中心是运动平面中的一点，所有其他点在特定时刻都围绕该点旋转。平面的连续运动对于时间参数的每个值都有一个瞬时中心。这会生成一条称为移动中心线的曲线。
The instant center of rotation (also known as instantaneous velocity center, instantaneous center, or pole of planar displacement) of a body undergoing planar movement is a point that has zero velocity at a particular instant of time. At this instant, the velocity vectors of the other points in the body generate a circular displacement field around this center of rotation which is identical to what is generated by a pure rotation. Planar movement of a body is often described using a plane figure moving in a two-dimensional plane. The instant center is the point in the moving plane around which all other points are rotating at a specific instant of time. The continuous movement of a plane has an instant center for every value of the time parameter. This generates a curve called the moving centrode.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 牛顿运动定律是描述物体运动与作用在其上的力之间关系的三个物理定律。这些定律为牛顿力学提供了基础，可以解释如下：物体保持静止状态，或以恒定速度沿直线运动，除非受到力的作用。在任何时刻，物体上的净力等于物体的加速度乘以其质量，或者等效地，物体的动量随时间变化的速率。如果两个物体相互施加力，这些力的大小相同但方向相反。运动三大定律最初由艾萨克·牛顿 (Isaac Newton) 在其 1687 年出版的《Philosophiæ Naturalis Principia Mathematica》（自然哲学的数学原理）中首次提出。
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force. At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions. The three laws of motion were first stated by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), originally published in 1687.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在物理学中，牛顿动力学（也称为牛顿力学）是根据牛顿运动定律研究粒子或小物体的动力学。
In physics, Newtonian dynamics (also known as Newtonian mechanics) is the study of the dynamics of a particle or a small body according to Newton's laws of motion.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 牛顿秒（也称为牛顿秒；符号：N⋅s 或 N s）是国际单位制 (SI) 中的冲量单位。它在量纲上等于动量单位千克米每秒 (kg·m/s)。一牛顿秒对应于施加一牛顿的力一秒。 F → ⋅ t = Δ m v → {\displaystyle {\vec {F}}\cdot t=\Delta m{\vec {v}}} 如果力在特定时间间隔内使质量加速，则可用于确定质量的合成速度。
The newton-second (also newton second; symbol: N⋅s or N s) is the unit of impulse in the International System of Units (SI). It is dimensionally equivalent to the momentum unit kilogram-metre per second (kg⋅m/s). One newton-second corresponds to a one-newton force applied for one second. F → ⋅ t = Δ m v → {\displaystyle {\vec {F}}\cdot t=\Delta m{\vec {v}}} It can be used to identify the resultant velocity of a mass if a force accelerates the mass for a specific time interval.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在力学中，物体的位置与时间图的导数等于物体的速度。在国际单位制中，移动物体的位置以相对于原点的米为单位，而时间以秒为单位。将位置放在 y 轴上，将时间放在 x 轴上，曲线的斜率由下式给出： v = Δ y Δ x = Δ s Δ t 。 {\displaystyle v={\frac {\Delta y}{\Delta x}}={\frac {\Delta s}{\Delta t}}.} 这里 s {\displaystyle s} 是物体的位置，t {\displaystyle t} 是时间。
In mechanics, the derivative of the position vs. time graph of an object is equal to the velocity of the object. In the International System of Units, the position of the moving object is measured in meters relative to the origin, while the time is measured in seconds. Placing position on the y-axis and time on the x-axis, the slope of the curve is given by: v = Δ y Δ x = Δ s Δ t . {\displaystyle v={\frac {\Delta y}{\Delta x}}={\frac {\Delta s}{\Delta t}}.} Here s {\displaystyle s} is the position of the object, and t {\displaystyle t} is the time.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在经典力学中，牛顿旋转轨道定理确定了将粒子的角速度乘以系数 k 而不影响其径向运动所需的中心力的类型（图 1 和 2）。牛顿应用他的定理来理解在月球和行星上观测到的轨道整体自转（近轴进动，图 3）。术语“径向运动”表示朝向或远离力中心的运动，而角运动垂直于径向运动。艾萨克·牛顿在其 1687 年首次出版的《自然哲学数学原理》第一卷的命题 43-45 中推导出了这个定理。在命题 43 中，他表明附加的力必须是中心力，其大小仅取决于粒子与空间中固定点（中心）之间的距离 r。
In classical mechanics, Newton's theorem of revolving orbits identifies the type of central force needed to multiply the angular speed of a particle by a factor k without affecting its radial motion (Figures 1 and 2). Newton applied his theorem to understanding the overall rotation of orbits (apsidal precession, Figure 3) that is observed for the Moon and planets. The term "radial motion" signifies the motion towards or away from the center of force, whereas the angular motion is perpendicular to the radial motion. Isaac Newton derived this theorem in Propositions 43–45 of Book I of his Philosophiæ Naturalis Principia Mathematica, first published in 1687. In Proposition 43, he showed that the added force must be a central force, one whose magnitude depends only upon the distance r between the particle and a point fixed in space (the center).
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在经典力学中，如果作用在系统上的力可以以特定的、特别方便的数学形式建模，则物理系统被称为单基因系统。物理学中通常研究的系统是单基因的。该术语由科尼利厄斯·兰佐斯 (Cornelius Lanczos) 在他的著作《力学变分原理》(1970) 中引入。在拉格朗日力学中，单基因性质是某些不同公式在数学上等价的必要条件。如果一个物理系统既是完整系统又是单基因系统，那么就可以从达朗贝尔原理推导出拉格朗日方程；也可以从哈密顿原理推导出拉格朗日方程。
In classical mechanics, a physical system is termed a monogenic system if the force acting on the system can be modelled in a particular, especially convenient mathematical form. The systems that are typically studied in physics are monogenic. The term was introduced by Cornelius Lanczos in his book The Variational Principles of Mechanics (1970). In Lagrangian mechanics, the property of being monogenic is a necessary condition for certain different formulations to be mathematically equivalent. If a physical system is both a holonomic system and a monogenic system, then it is possible to derive Lagrange's equations from d'Alembert's principle; it is also possible to derive Lagrange's equations from Hamilton's principle.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 由英国工程师克里斯托弗·科克雷尔 (Christopher Cockerell) 发现，动量幕是一种独特而有效的方法，可以通过气垫将车辆悬浮在水面或陆地上方，从而减少车辆与其行驶表面（无论是水还是陆地）之间的摩擦。气垫船正是基于这种悬浮原理，克里斯托弗·科克雷尔开始将他的动量幕理论应用于气垫船，以提高其克服行驶中摩擦的能力。将车辆悬浮在地面/水面上方以减少阻力并不是一个新概念。约翰·桑尼克罗夫特 (John Thornycroft) 于 1877 年发现，将空气困在船体下方，或用风箱将空气泵入船体下方，可以减少船体上的摩擦力，从而提高船的最高可达速度。然而，当时的技术不足以让桑尼克罗夫特的想法得到进一步发展。
Discovered by British engineer Christopher Cockerell, the momentum curtain is a unique and efficient way to reduce friction between a vehicle and its surface of travel, be it water or land, by levitating the vehicle above this surface via a cushion of air. It is this principle of levitation upon which a hovercraft is based, and Christopher Cockerell set about applying his momentum curtain theory to hovercraft to increase their abilities in overcoming friction in travel. Levitating a vehicle above the ground/water to reduce its drag was not a new concept. John Thornycroft, in 1877, discovered that trapping air beneath a ship's hull, or pumping air beneath it with bellows, decreased the effects of friction upon the hull thereby increasing the ship's top attainable speeds. However, technology at the time was insufficient for Thornycroft's ideas to be developed further.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在物理学中，n 体问题是预测一组天体在引力作用下的个体运动的问题。解决这个问题的动机是了解太阳、月球、行星和可见恒星的运动。经典物理问题可以表述如下：有限数量粒子系统中的每个粒子都受到来自所有其他粒子的牛顿引力的作用，而不受到其他力的作用。如果给定系统的初始状态，粒子将如何运动？二体问题已经解决，下面讨论。对于三个或更多物体，只有在特定情况下才能完全解决问题。一般来说，问题是混沌的，只能用数值方法求解。广义相对论中的 n 体问题要解决起来要困难得多。
In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally. Solving this problem has been motivated by the desire to understand the motions of the Sun, Moon, planets, and visible stars. The classical physical problem can be stated as follows: Each particle in a system of a finite number of particles is subjected to a Newtonian gravitational attraction from all the other particles, and to no other forces. If the initial state of the system is given, how will the particles move? The two-body problem has been solved and is discussed below. For three or more bodies the problem can only be solved completely in particular cases. In general, the problem is chaotic and can only be solved numerically. The n-body problem in general relativity is considerably more difficult to solve.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ n 体编排是 n 体问题的周期性解决方案，其中所有物体沿着单个轨道均匀分布。该术语由 Chenciner 和 Montgomery 于 2000 年首次提出。其中一种轨道是圆形轨道，在等边三角形的角上具有相等的质量；另一种是 8 字形轨道，由 Cristopher Moore 于 1993 年首次以数值方式发现，随后由 Chenciner 和 Montgomery 证明其存在。编排可以使用变分方法来发现，最近，拓扑方法已被用来尝试在平面情况下进行分类。掌握特定解决方案（例如编排）的知识非常有用，因为不可能通过显式方法解决 N > 2 的 N 体问题。
An n-body choreography is a periodic solution to the n-body problem in which all the bodies are equally spread out along a single orbit. The term was originated in 2000 by Chenciner and Montgomery. One such orbit is a circular orbit, with equal masses at the corners of an equilateral triangle; another is the figure-8 orbit, first discovered numerically in 1993 by Cristopher Moore and subsequently proved to exist by Chenciner and Montgomery. Choreographies can be discovered using variational methods, and more recently, topological approaches have been used to attempt a classification in the planar case. Having knowledge of specific solutions such as choreographies can be incredibly useful as it is not possible to solve the N-body problem for N > 2 through explicit means.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 剪切带（shear band）是材料中一个狭窄的强剪切应变区，通常在延性材料严重变形时出现，具有可塑性。剪切带会比材料的其他部位先失去韧性，剪切带中发生的极端变形可能导致材料严重的损坏和断裂，因此研究剪切带如何形成是一个对材料应用非常重要的课题，20世纪中叶以来变形局部化（localization of deformation）一直被密集研究。
In solid mechanics, a shear band (or, more generally, a strain localization) is a narrow zone of intense strain due to shearing, usually of plastic nature, developing during severe deformation of ductile materials. As an example, a soil (overconsolidated silty-clay) specimen is shown in Fig. 1, after an axialsymmetric compression test. Initially the sample was cylindrical in shape and, since symmetry was tried to be preserved during the test, the cylindrical shape was maintained for a while during the test and the deformation was homogeneous, but at extreme loading two X-shaped shear bands had formed and the subsequent deformation was strongly localized (see also the sketch on the right of Fig. 1).
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View content license ↗ 断裂力学（Fracture mechanics）是研究含裂纹构件强度与寿命的一门固体力学的新分支，结构损伤容限设计的理论基础。可以分为线弹性断裂力学与弹塑性断裂力学两大类别，前者适用于裂纹尖端附近小范围屈服的情况；而后者适用于裂纹尖端附近大范围屈服的情况。就目前情况而言，弹塑性断裂力学发展很快，但是线弹性断裂力学在结构损伤容限设计中仍然占据重要地位。 在线弹性断裂力学中，最重要的力学参量是应力强度因子，它控制裂纹尖端场附近的应力场和位移场。
Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. Theoretically, the stress ahead of a sharp crack tip becomes infinite and cannot be used to describe the state around a crack. Fracture mechanics is used to characterise the loads on a crack, typically using a single parameter to describe the complete loading state at the crack tip. A number of different parameters have been developed. When the plastic zone at the tip of the crack is small relative to the crack length the stress state at the crack tip is the result of elastic forces within the material and is termed linear elastic fracture mechanics (LEFM) and can be characterised using the stress intensity factor K {\displaystyle K} . Although the load on a crack can be arbitrary, in 1957 G.
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View content license ↗ 位错（英语：dislocation），在材料科学中，指晶体材料的一种内部微观缺陷，即原子的局部不规则排列（晶体缺陷）。从几何角度看，位错属于一种线缺陷，可视为晶体中已滑移部分与未滑移部分的分界线，其存在对材料的物理性能，尤其是力学性能，具有极大的影响。“位错”这一概念最早由意大利数学家和物理学家维托·伏尔特拉于1905年提出。 理想位错主要有三种形式：刃位错（edge dislocation）和 螺旋位错（screw dislocation）及混合位错（mixed dislocation）兼有前面两者的特征。 数学上，位错属于一种拓扑缺陷，有时称为“孤立子”或“孤子”。这一理论可以解释实际晶体中位错的行为：可以在晶体中移动位置，但自身的种类和特征在移动中保持不变；方向（伯格斯矢量）相反的两个位错移动到同一点，则会双双消失，或称“湮灭”，若没有与其他位错发生作用或移到晶体表面，那么任何单个位错都不会自行“消失”（即伯格斯矢量始终保持守恒）。
In materials science, a dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allows atoms to slide over each other at low stress levels and is known as glide or slip. The crystalline order is restored on either side of a glide dislocation but the atoms on one side have moved by one position. The crystalline order is not fully restored with a partial dislocation. A dislocation defines the boundary between slipped and unslipped regions of material and as a result, must either form a complete loop, intersect other dislocations or defects, or extend to the edges of the crystal. A dislocation can be characterised by the distance and direction of movement it causes to atoms which is defined by the Burgers vector. Plastic deformation of a material occurs by the creation and movement of many dislocations. The number and arrangement of dislocations influences many of the properties of materials.
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View content license ↗ 晶粒边界（英语：grain boundary），简称晶界，指多晶材料中晶粒之间的接合区域。在结晶学中晶粒边界是一种二维的晶体缺陷。晶粒边界出现在结构相同方向不同的微晶区域里，通过化学腐蚀可以使之在晶体表面显现。晶粒边界有小角度晶界和大角度晶界之分。当两个微晶区域之间的角度差值大于15度时，我们称之为大角度晶界。大角度晶界阻碍了位错的形成，从而影响了相邻晶粒。因此大角度晶界对金属材料的机械特性影响显著。在大多数情况下，晶粒边界会导致强度的提高，也就是说细粒度晶体更加坚固，但是析出物（特别是在容易在晶粒边界聚集的氧化物）同时也会削弱晶体强度。
In materials science, a grain boundary is the interface between two differently oriented grains, or crystallites, of the same phase in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material. Most grain boundaries are preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep. On the other hand, grain boundaries disrupt the motion of dislocations through a material, so reducing crystallite size is a common way to improve mechanical strength, as described by the Hall–Petch relationship.
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View content license ↗ 在材料科学中，硬度（反义词：柔软度）是对局部塑性变形的抵抗力的量度，例如通过按压或磨损机械引起的压痕（在某个区域上）或划痕（线性）。一般来说，不同材质的硬度不同；例如，钛和铍等硬金属比钠和金属锡等软金属或木材和普通塑料更硬。宏观硬度一般以较强的分子间键为特征，但固体材料在受力作用下的行为却很复杂；因此，硬度可以通过不同的方式测量，例如划痕硬度、压痕硬度和回弹硬度。硬度取决于延展性、弹性刚度、塑性、应变、强度、韧性、粘弹性和粘度。
In materials science, hardness (antonym: softness) is a measure of the resistance to localized plastic deformation, such as an indentation (over an area) or a scratch (linear), induced mechanically either by pressing or abrasion. In general, different materials differ in their hardness; for example hard metals such as titanium and beryllium are harder than soft metals such as sodium and metallic tin, or wood and common plastics. Macroscopic hardness is generally characterized by strong intermolecular bonds, but the behavior of solid materials under force is complex; therefore, hardness can be measured in different ways, such as scratch hardness, indentation hardness, and rebound hardness. Hardness is dependent on ductility, elastic stiffness, plasticity, strain, strength, toughness, viscoelasticity, and viscosity.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 温度系数（temperature coefficient）是指在温度变化1K时，特定物理量的相对变化。 以下的公式中，R为特定的物理量，T为量测物理量时的温度，T0为参考温度，ΔT为量测温度及参考温度的温度差，α为（线性）温度系数。则物理量可以用以下公式表示： R ( T ) = R ( T 0 ) ( 1 + α Δ T ) {\displaystyle \operatorname {R} (T)=\operatorname {R} (T_{0})(1+\alpha \Delta T)} 此处α的量纲为温度的倒数（1/K或K−1）。 以上式子的物理量和温度成线性关系，若物理量和温度的多项式或对数成正比，也可以在一定温度范围内计算温度系数，近似此范围内的物理量变化。若物理量是随温度指数增长或指数衰减（例如阿伦尼乌斯方程），只能在一个很小的温度范围内计算温度系数。 温度系数会随应用领域的不同而不同，例如核能、电子学或磁学均有其温度系数。物体的弹性模量也会随温度而变化，一般弹性模量会随温度升高而下降。
A temperature coefficient describes the relative change of a physical property that is associated with a given change in temperature. For a property R that changes when the temperature changes by dT, the temperature coefficient α is defined by the equation below: d R R = α d T {\displaystyle {\frac {dR}{R}}=\alpha \,dT} Here α has the dimension of an inverse temperature and can be expressed e.g. in 1/K or K−1.
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View content license ↗ 菲克定律（英语：Fick's law）描述扩散作用，可以使用这条定律来求得扩散系数：D。定律由德国生理学家阿道夫·菲克于1855年推导出来。
Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, D {\displaystyle D} . Fick's first law can be used to derive his second law, which in turn is identical to the diffusion equation. Fick's first law: Movement of particles from high to low concentration (diffusive flux) is directly proportional to the particle's concentration gradient. Fick's second law: Prediction of change in concentration gradient with time due to diffusion. A diffusion process that obeys Fick's laws is called normal or Fickian diffusion; otherwise, it is called anomalous diffusion or non-Fickian diffusion.
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View content license ↗ 开尔文-沃伊特材料（Kelvin–Voigt material），又称沃伊特材料，是表现典型橡胶特性的最简单黏弹性模型。该材料在长时间尺度（慢速形变）下表现为纯弹性，但在快速形变时会产生额外的阻力。该模型由英国物理学家开尔文勋爵于1865年及德国物理学家沃尔德马·沃伊特于1890年分别独立提出。 开尔文-沃伊特模型（或称沃伊特模型）由一个纯黏性阻尼器和一个纯弹性弹簧并联组成。 若将这两个元件串联，则得到麦克斯韦模型。
A Kelvin–Voigt material, also called a Voigt material, is the simplest model viscoelastic material showing typical rubbery properties. It is purely elastic on long timescales (slow deformation), but shows additional resistance to fast deformation. The model was developed independently by the British physicist Lord Kelvin in 1865 and by the German physicist Woldemar Voigt in 1890.
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View content license ↗ 麦克斯韦模型（英语：Maxwell model）是用于描述材料粘弹性的一种模型。麦克斯韦由一个纯弹性的弹簧和一个纯黏性的黏壶（阻尼器）串联而成，其中的弹簧符合胡克定律，用于描述材料的弹性方面性质；而黏壶符合牛顿流体特征，代表黏性方面性质。1867年，詹姆斯·麦克斯韦提出了这一模型，符合这一模型的流体也被称为麦克斯韦流体。如果将弹簧和黏壶并联，则被称为开尔文-沃伊特模型。
In fluid mechanics, a Maxwell model is the simplest model viscoelastic material showing properties of a typical liquid. It shows viscous flow on the long timescale, but additional elastic resistance to fast deformations. It is named for James Clerk Maxwell who proposed the model in 1867. It is also known as a Maxwell fluid. A generalization of the scalar relation to a tensor equation lacks motivation from more microscopic models and does not comply with the concept of material objectivity. However, these criteria are fulfilled by the Upper-convected Maxwell model.
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View content license ↗ 固溶强化（英语：Solid solution strengthening）是一种利用加入溶质原子形成固溶体，并且提高整体强度的方法。加入溶质原子会降低位错周围的内应力，阻挡位错移动而使得变形更不易发生，以达到强化的效果。
In metallurgy, solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. The technique works by adding atoms of one element (the alloying element) to the crystalline lattice of another element (the base metal), forming a solid solution. The local nonuniformity in the lattice due to the alloying element makes plastic deformation more difficult by impeding dislocation motion through stress fields. In contrast, alloying beyond the solubility limit can form a second phase, leading to strengthening via other mechanisms (e.g. the precipitation of intermetallic compounds).
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