The mutual energies and the reciprocity law
Abstract
For a system of two degrees of freedom the four analogue circuits - two dual mechanical and two dual electrical - are discussed. The Lagrange-Rayleigh-equation developed for displacements as coordinates is extended to the other three types. From the uniequivocal mutual energies follows the reciprocity-law in all its variations. By expressing it as an equation of powers it shows that the oscillating parts of the mutual powers are equal both in amplitude and phase. If furthermore the excitations are either in phase or in antiphase, or if the input impedances are real, the mutual powers are even equal in each moment inclusive the average values. By change of sign the condition for the mutual powers at ideal reversible transducers (lever, gyroscope, transformer, gyrator) results from which the conditions for the transducer-coefficients may be derived.
- Publication:
-
Ingenieur Archiv
- Pub Date:
- 1976
- Bibcode:
- 1976IngAr..45..371C
- Keywords:
-
- Analog Circuits;
- Electric Networks;
- Energy Methods;
- Mechanical Oscillators;
- Reciprocal Theorems;
- Transducers;
- Degrees Of Freedom;
- Differential Equations;
- Phase Deviation;
- Rayleigh Equations;
- Physics (General)