“superposition principle”的概念、定义、翻译、参考文献-科学参考

superposition principle

Physics

A general principle of linear systems that when applied to wave phenomena asserts that the combined effect of any number of interacting waves at a point may be obtained by the algebraic summation of the amplitudes of all the waves at the point. For example, the superposition of two oscillations x₁ and x₂, both of frequency ν‎, produces a disturbance of the same frequency. The amplitude and phase angle of the resulting disturbance are functions of the component amplitudes and phases. Thus, if

$x_{1} = a_{1} sin (2 {π ν + δ}_{1})$

and

$x_{2} = a_{2} sin (2 {π ν + δ}_{2})$

the resultant disturbance, x, will be given by:

$x = A sin (2 π ν + Δ),$

where amplitude A and phase angle Δ‎ are both functions of a₁, a₂, δ‎₁, and δ‎₂.

Mathematics

If y₁ and y₂ are solutions of a homogeneous linear differential equation Ly = 0, then c₁y₁+ c₂y₂ is also a solution, by definition of L being linear. The same may also be true of an infinite sum

$\sum_{k = 0}^{\infty} c_{k} y_{k}$

of solutions y_k, though issues of convergence and differentiability may need addressing carefully. Given a homogeneous linear boundary value problem, a general solution may be sought as an infinite sum of separable solutions with the coefficients c_k being determined using Fourier analysis.

Electronics and Electrical Engineering

The principle that all linear functions satisfy two properties: additivity and homogeneity. Additivity is the property that adding the result of applying the function to two inputs is the same as applying the function to the sum of the inputs.
$f (x) + f (y) = f (x + y)$
Homogeneity is the property that multiplying the result of applying a function to an input by a fixed value is the same as applying the function to the input multiplied by that value.
$k \times f (x) = f (k \times x)$

单词	superposition principle
释义	superposition principle Physics A general principle of linear systems that when applied to wave phenomena asserts that the combined effect of any number of interacting waves at a point may be obtained by the algebraic summation of the amplitudes of all the waves at the point. For example, the superposition of two oscillations x₁ and x₂, both of frequency ν‎, produces a disturbance of the same frequency. The amplitude and phase angle of the resulting disturbance are functions of the component amplitudes and phases. Thus, if $x_{1} = a_{1} sin (2 {π ν + δ}_{1})$ and $x_{2} = a_{2} sin (2 {π ν + δ}_{2})$ the resultant disturbance, x, will be given by: $x = A sin (2 π ν + Δ),$ where amplitude A and phase angle Δ‎ are both functions of a₁, a₂, δ‎₁, and δ‎₂. Mathematics If y₁ and y₂ are solutions of a homogeneous linear differential equation Ly = 0, then c₁y₁+ c₂y₂ is also a solution, by definition of L being linear. The same may also be true of an infinite sum $\sum_{k = 0}^{\infty} c_{k} y_{k}$ of solutions y_k, though issues of convergence and differentiability may need addressing carefully. Given a homogeneous linear boundary value problem, a general solution may be sought as an infinite sum of separable solutions with the coefficients c_k being determined using Fourier analysis. Electronics and Electrical Engineering The principle that all linear functions satisfy two properties: additivity and homogeneity. Additivity is the property that adding the result of applying the function to two inputs is the same as applying the function to the sum of the inputs. $f (x) + f (y) = f (x + y)$ Homogeneity is the property that multiplying the result of applying a function to an input by a fixed value is the same as applying the function to the input multiplied by that value. $k \times f (x) = f (k \times x)$
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