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 abstractio ...
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 function (mathematics), mathematical function that mathematical model, models the system's output for each possible ...
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. It consists of mechanically exciting a studied component in such a way to target the Normal mode, modeshapes of the structure, and recording the vibration ...
this is known as Maxwell's reciprocity theorem. In electromagnetism the concept is known as
Lorentz reciprocity, 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
In mathematics, a linear combination or superposition is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of ''x'' and ''y'' would be any expression of the form ...
, symmetry and anti-symmetry, it can be used to resolve complex load conditions.
References
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Applied mathematics
Engineering concepts