Calculus of variations of Herglotz type
We consider several problems based on Herglotz’s generalized variational problem. We dedicate two chapters to extensions on Herglotz’s generalized variational problem to higher-order and first-order problems with time delay, using a variational approach. In the last four chapters, we rewrite Herglot...
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| Format: | doctoralThesis |
| Language: | eng |
| Published: |
2018
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10773/22503 |
| Country: | Portugal |
| Oai: | oai:ria.ua.pt:10773/22503 |
| Summary: | We consider several problems based on Herglotz’s generalized variational problem. We dedicate two chapters to extensions on Herglotz’s generalized variational problem to higher-order and first-order problems with time delay, using a variational approach. In the last four chapters, we rewrite Herglotz's type problems in the optimal control form and use an optimal control approach. We prove generalized higher- order Euler-Lagrange equations, first without and then with time delay; higher-order natural boundary conditions; Noether's first theorem for the first-order problem of Herglotz with time delay; Noether's first theorem for higher-order problems of Herglotz without and with time delay; and existence of Noether currents as a version of Noether's second theorem of optimal control. |
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