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On complementary variational principles in linear vibrations

โœ Scribed by Bruce H. Karnopp

Publisher
Elsevier Science
Year
1967
Tongue
English
Weight
598 KB
Volume
284
Category
Article
ISSN
0016-0032

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โœฆ Synopsis

Two, complementary, variational

principles can be applied in the analysis of dynamic systems. Often it appears to be difficult to formulate a given system in terms of the so-called "complementary variational principle." In the case of a linear, finite dimensional system, however, we can always obtain a complementary formulation of the problem by means of a repeated application of the Legendre transformation either to the system Lagrangian or, in the case of a system with ignorable coordinates, to the system Routhian.

๐Ÿ“œ SIMILAR VOLUMES

Remarks on variational principles in ela
Remarks on variational principles in elastodynamics
โœ Yu Chen ๐Ÿ“‚ Article ๐Ÿ“… 1964 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 256 KB

Two principles are basic in the variational formulations of elasticity. Green's "variation for displacements" leads to the principle of minimum potential energy, whereas Castigliano's "variation for stresses" leads to the principle of minimum complementary energy. In the small vibration of elastic b