On hamilton's principle for discrete and continuous systems: A convolved action principle
| Autor: | Antonios Charalambopoulos, V.K. Kalpakides |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
010308 nuclear & particles physics
Dirac delta function Statistical and Nonlinear Physics 01 natural sciences Action (physics) Fractional calculus Convolution symbols.namesake Variational principle Product (mathematics) 0103 physical sciences symbols Initial value problem Applied mathematics Hamilton's principle 010307 mathematical physics Mathematical Physics Mathematics |
| Zdroj: | Reports on Mathematical Physics. 87:225-248 |
| ISSN: | 0034-4877 |
| DOI: | 10.1016/s0034-4877(21)00027-6 |
| Popis: | In an attempt to generalize Hamilton's principle, an action functional is proposed which, unlike the standard version of the principle, accounts properly for all initial data and the possible presence of dissipation. To this end, the convolution is used instead of the L2 inner product so as to eliminate the undesirable end temporal condition of Hamilton's principle. Also, fractional derivatives are used to account for dissipation and the Dirac delta function is exploited so as the initial velocity can be inherently set into the variational setting. The proposed approach applies to both finite- and infinite-dimensional systems. |
| Databáze: | OpenAIRE |
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