Reciprocity in
linear system
In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator.
Linear systems typically exhibit features and properties that are much simpler than the nonlinear case.
As a mathematical abstracti ...
s is the principle that a response Rab, measured at a location (and direction if applicable) a, when the system has an excitation signal applied at a location (and direction if applicable) b, is exactly equal to Rba which is the response at location b, when that same excitation is applied at a. This applies for all frequencies of the excitation signal. If Hab is the
transfer function
In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that theoretically models the system's output for each possible input. They are widely used ...
between a and b then Hab = Hba, if the system is linear.
In the special case of a
modal analysis
Modal analysis is the study of the dynamic properties of systems in the frequency domain. Examples would include measuring the vibration of a car's body when it is attached to a shaker, or the noise pattern in a room when excited by a loudspeake ...
this is known as Maxwell's reciprocity theorem. In electromagnetism the concept is known as
Lorentz reciprocity
In classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities (sources) and the resulting electromagnetic fields in Maxwell's equations for time-invariant l ...
, a special case of which is the
reciprocity theorem of electrical networks.
The reciprocity principle is also used in the analysis of structures.
When combined with
superposition
Superposition may refer to:
Science and mathematics
* Law of superposition in geology and archaeology, which states that sedimentary layers are deposited in a time sequence, with the oldest on the bottom and the youngest on the top
* Superposit ...
, symmetry and anti-symmetry, it can be used to resolve complex load conditions.
References
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Applied mathematics
Engineering concepts