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On the variational principles of mechanics

✍ Scribed by V.V. Kozlov

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
201 KB
Volume
74
Category
Article
ISSN
0021-8928

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✦ Synopsis

Variational principles, generalizing the classical d'Alembert-Lagrange, HΓΆlder, and Hamilton-Ostrogradskii principles, are established. After the addition of anisotropic dissipative forces and taking the limit, when the coefficient of viscous friction tends to infinity, these variational principles transform into the classical principles, which describe the motion of systems with constraints. New variational relations are established for searching for the periodic trajectories of the reversible equations of dynamics.

πŸ“œ SIMILAR VOLUMES

The Four Variational Principles of Mecha
The Four Variational Principles of Mechanics
✍ C.G. Gray; G. Karl; V.A. Novikov πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 564 KB

We argue that there are four basic forms of the variational principles of mechanics: Hamilton's least action principle (HP), the generalized Maupertuis principle (MP), and their two reciprocal principles, RHP and RMP. This set is invariant under reciprocity and Legendre transformations. One of these