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第1行： − 此词条暂由彩云小译翻译，翻译字数共1565，未经人工整理和审校，带来阅读不便，请见谅。+ − + + + − + − 几乎[来自远方的平面波(对角线)和鸭子尾迹的波的叠加。线性只在水中大致适用，并且只适用于相对于波长振幅较小的波。]+ + + + 第20行：
第25行： + + − 叠加叠加原理，也被称为叠加性质，指出，对于所有线性系统，由两个或更多刺激引起的净反应是由每个刺激单独引起的反应的总和。因此，如果输入 a 产生响应 x，输入 b 产生响应 y，那么输入(a + b)产生响应(x + y)。+ + + 第58行：
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此词条暂由水流心不竞初译，翻译字数共，未经审校，带来阅读不便，请见谅。
{{short description|Fundamental physics principle stating that physical solutions of linear systems are linear}}
{{short description|Fundamental physics principle stating that physical solutions of linear systems are linear}}
{{简述}说明线性系统的物理解是线性的基本物理原理}}
{{About|the superposition principle in linear systems|other uses|Superposition (disambiguation)}}
{{About|the superposition principle in linear systems|other uses|Superposition (disambiguation)}}
{{关于|线性系统中的叠加原理|其他用途|叠加（消歧）}}
[[File:Anas platyrhynchos with ducklings reflecting water.jpg|thumb|right|Superposition of almost [[plane wave]]s (diagonal lines) from a distant source and waves from the [[wake]] of the [[duck]]s. [[Linearity]] holds only approximately in water and only for waves with small amplitudes relative to their wavelengths.]]
[[File:Anas platyrhynchos with ducklings reflecting water.jpg|thumb|right|Superposition of almost [[plane wave]]s (diagonal lines) from a distant source and waves from the [[wake]] of the [[duck]]s. [[Linearity]] holds only approximately in water and only for waves with small amplitudes relative to their wavelengths.]]
[[文件：Anas platyrhynchos小鸭在倒影水.jpg|拇指|右|来自远源的几乎[[平面波]]s（对角线）和来自[[鸭]]s的[[尾迹]]的波的叠加。[[线性]]仅在水中近似成立，并且仅适用于相对于其波长振幅较小的波。]]
Superposition of almost [[plane waves (diagonal lines) from a distant source and waves from the wake of the ducks. Linearity holds only approximately in water and only for waves with small amplitudes relative to their wavelengths.]]
Superposition of almost [[plane waves (diagonal lines) from a distant source and waves from the wake of the ducks. Linearity holds only approximately in water and only for waves with small amplitudes relative to their wavelengths.]]
来自远处震源的几乎是[[平面波（对角线）和鸭子尾迹的波的叠加。线性仅在水中近似成立，且仅适用于相对于波长振幅较小的波。]]
[[File:Rolling animation.gif|right|thumb| [[Rolling]] motion as superposition of two motions. The rolling motion of the wheel can be described as a combination of two separate motions: [[translation (geometry)|translation]] without [[rotation]], and rotation without translation.]]
[[File:Rolling animation.gif|right|thumb| [[Rolling]] motion as superposition of two motions. The rolling motion of the wheel can be described as a combination of two separate motions: [[translation (geometry)|translation]] without [[rotation]], and rotation without translation.]]
[[文件：Rolling animation.gif|右|拇指|[[滚动]]运动是两个运动的叠加。车轮的滚动运动可以描述为两个独立运动的组合：[[平移（几何）|平移]]无[[旋转]]和旋转无平移。]]
[[Rolling motion as superposition of two motions. The rolling motion of the wheel can be described as a combination of two separate motions: translation without rotation, and rotation without translation.]]
[[Rolling motion as superposition of two motions. The rolling motion of the wheel can be described as a combination of two separate motions: translation without rotation, and rotation without translation.]]
The '''superposition principle''',<ref>The Penguin Dictionary of Physics, ed. Valerie Illingworth, 1991, Penguin Books, London</ref> also known as '''superposition property''', states that, for all [[linear system]]s, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input ''A'' produces response ''X'' and input ''B'' produces response ''Y'' then input (''A'' + ''B'') produces response (''X'' + ''Y'').
The '''superposition principle''',<ref>The Penguin Dictionary of Physics, ed. Valerie Illingworth, 1991, Penguin Books, London</ref> also known as '''superposition property''', states that, for all [[linear system]]s, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input ''A'' produces response ''X'' and input ''B'' produces response ''Y'' then input (''A'' + ''B'') produces response (''X'' + ''Y'').
“‘叠加原理’”，<ref>The Penguin Dictionary of Physics, ed. Valerie Illingworth, 1991, Penguin Books, London</ref>也称为“‘叠加性质’”，指出，对于所有的[[线性系统]]，两个或多个刺激引起的净反应是每个刺激单独引起的反应的总和。因此，如果输入“A”产生响应“X”，输入“B”产生响应“Y”，则输入（“A”+“B”）产生响应（“X”+“Y”）。
The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input A produces response X and input B produces response Y then input (A + B) produces response (X + Y).
The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input A produces response X and input B produces response Y then input (A + B) produces response (X + Y).
叠加原理，也被称为叠加性质，指出，对于所有线性系统，由两个或更多刺激引起的净反应是由每个刺激单独引起的反应的总和。因此，如果输入 a 产生响应 x，输入 b 产生响应 y，那么输入(a + b)产生响应(x + y)。
A [[function (mathematics)|function]] <math>F(x)</math> that satisfies the superposition principle is called a [[linear function]]. Superposition can be defined by two simpler properties; [[additive map|additivity]] and [[homogeneous function|homogeneity]]
A [[function (mathematics)|function]] <math>F(x)</math> that satisfies the superposition principle is called a [[linear function]]. Superposition can be defined by two simpler properties; [[additive map|additivity]] and [[homogeneous function|homogeneity]]
满足叠加原理的[[函数（数学）|函数]]<math>F(x)</math>称为[[线性函数]]。叠加可以用两个简单的性质来定义；[[加性映射|可加性]]和[[齐次函数|齐性]]
A function <math>F(x)</math> that satisfies the superposition principle is called a linear function. Superposition can be defined by two simpler properties; additivity and homogeneity
A function <math>F(x)</math> that satisfies the superposition principle is called a linear function. Superposition can be defined by two simpler properties; additivity and homogeneity
This principle has many applications in [[physics]] and [[engineering]] because many physical systems can be modeled as linear systems. For example, a [[beam (structure)|beam]] can be modeled as a linear system where the input stimulus is the [[structural load|load]] on the beam and the output response is the deflection of the beam. The importance of linear systems is that they are easier to analyze mathematically; there is a large body of mathematical techniques, [[frequency domain]] [[linear transform]] methods such as [[Fourier transform|Fourier]], [[Laplace transform]]s, and [[linear operator]] theory, that are applicable. Because physical systems are generally only approximately linear, the superposition principle is only an approximation of the true physical behaviour.
This principle has many applications in [[physics]] and [[engineering]] because many physical systems can be modeled as linear systems. For example, a [[beam (structure)|beam]] can be modeled as a linear system where the input stimulus is the [[structural load|load]] on the beam and the output response is the deflection of the beam. The importance of linear systems is that they are easier to analyze mathematically; there is a large body of mathematical techniques, [[frequency domain]] [[linear transform]] methods such as [[Fourier transform|Fourier]], [[Laplace transform]]s, and [[linear operator]] theory, that are applicable. Because physical systems are generally only approximately linear, the superposition principle is only an approximation of the true physical behaviour.
这一原理在[[物理]]和[[工程]]中有许多应用，因为许多物理系统可以建模为线性系统。例如，[[梁（结构）|梁]]可以建模为线性系统，其中输入激励是梁上的[[结构荷载|荷载]]，输出响应是梁的挠度。线性系统的重要性在于它们更易于数学分析；有大量的数学技术，[[频域]][[线性变换]]方法，如[[傅立叶变换|傅立叶]]、[[拉普拉斯变换]]和[[线性算子]]理论，都是适用的。因为物理系统通常只是近似线性的，叠加原理只是真实物理行为的近似。
This principle has many applications in physics and engineering because many physical systems can be modeled as linear systems. For example, a beam can be modeled as a linear system where the input stimulus is the load on the beam and the output response is the deflection of the beam. The importance of linear systems is that they are easier to analyze mathematically; there is a large body of mathematical techniques, frequency domain linear transform methods such as Fourier, Laplace transforms, and linear operator theory, that are applicable. Because physical systems are generally only approximately linear, the superposition principle is only an approximation of the true physical behaviour.
This principle has many applications in physics and engineering because many physical systems can be modeled as linear systems. For example, a beam can be modeled as a linear system where the input stimulus is the load on the beam and the output response is the deflection of the beam. The importance of linear systems is that they are easier to analyze mathematically; there is a large body of mathematical techniques, frequency domain linear transform methods such as Fourier, Laplace transforms, and linear operator theory, that are applicable. Because physical systems are generally only approximately linear, the superposition principle is only an approximation of the true physical behaviour.
The superposition principle applies to ''any'' linear system, including [[algebraic equation]]s, [[linear differential equations]], and [[system of equations|systems of equations]] of those forms. The stimuli and responses could be numbers, functions, vectors, [[vector field]]s, time-varying signals, or any other object that satisfies [[vector space|certain axioms]]. Note that when vectors or vector fields are involved, a superposition is interpreted as a [[vector sum]].
The superposition principle applies to ''any'' linear system, including [[algebraic equation]]s, [[linear differential equations]], and [[system of equations|systems of equations]] of those forms. The stimuli and responses could be numbers, functions, vectors, [[vector field]]s, time-varying signals, or any other object that satisfies [[vector space|certain axioms]]. Note that when vectors or vector fields are involved, a superposition is interpreted as a [[vector sum]].
叠加原理适用于“任何”线性系统，包括这些形式的[[代数方程]]s、[[线性微分方程]]和[[方程组|方程组]]。刺激和反应可以是数字、函数、向量、[[vector field]]s、时变信号或满足[[vector space |某些公理]]的任何其他对象。注意，当涉及向量或向量场时，叠加被解释为[[向量和]]。
The superposition principle applies to any linear system, including algebraic equations, linear differential equations, and systems of equations of those forms. The stimuli and responses could be numbers, functions, vectors, vector fields, time-varying signals, or any other object that satisfies certain axioms. Note that when vectors or vector fields are involved, a superposition is interpreted as a vector sum.
The superposition principle applies to any linear system, including algebraic equations, linear differential equations, and systems of equations of those forms. The stimuli and responses could be numbers, functions, vectors, vector fields, time-varying signals, or any other object that satisfies certain axioms. Note that when vectors or vector fields are involved, a superposition is interpreted as a vector sum.