Creator 

Abstract or Summary 
 The generalized variational principle of Herglotz defines the functional whose extrema are sought by a differential equation rather than an integral. It reduces to the classical variational principle under classical conditions. The Noether theorems are not applicable to functionals defined by differential equations. For a system of differential equations derivable from the generalized variational principle of Herglotz, a first Noethertype theorem is proven, which gives explicit conserved quantities corresponding to the symmetries of the functional defined by the generalized variational principle of Herglotz. This theorem reduces to the classical first Noether theorem in the case when the generalized variational principle of
Herglotz reduces to the classical variational principle. Applications of the first Noethertype theorem are shown and specific examples are provided. A second Noethertype theorem is proven, providing a nontrivial identity corresponding to each infinitedimensional symmetry group of the functional defined by the generalized variational principle of Herglotz. This theorem reduces to the classical second Noether theorem when the generalized variational principle of Herglotz reduces to the classical variational principle. A new variational principle with several independent variables is defined. It reduces to Herglotz's generalized variational principle in the case of one independent
variable, time. It also reduces to the classical variational principle with several
independent variables, when only the spatial independent variables are present. Thus, it generalizes both. This new variational principle can give a variational description of processes involving physical fields. One valuable characteristic is that, unlike the classical variational principle with several independent variables, this variational principle gives a variational description of nonconservative processes even when the Lagrangian function is independent of time. This is not possible with the classical variational principle. The equations providing the extrema of the functional defined by this generalized variational principle are derived. They reduce to the classical EulerLagrange equations (in the case of several independent variables), when this new variational principle reduces to the classical variational principle with several independent variables. A first Noethertype theorem is proven for the generalized variational principle with several independent variables. One of its corollaries provides an explicit procedure for finding the conserved quantities corresponding to symmetries of the functional defined by this variational principle. This theorem reduces to the classical first Noether theorem in the case when the generalized variational principle with several independent variables reduces to the classical variational principle with several independent variables. It reduces to the first Noethertype theorem for Herglotz generalized variational principle when this generalized variational principle reduces to Herglotz's variational principle. A criterion for a transformation to be a symmetry of the functional defined by
the generalized variational principle with several independent variables is proven.
Applications of the first Noethertype theorem in the several independent variables
case are shown and specific examples are provided.

Resource Type 

Date Available 

Date Copyright 

Date Issued 

Degree Level 

Degree Name 

Degree Field 

Degree Grantor 

Commencement Year 

Advisor 

Academic Affiliation 

NonAcademic Affiliation 

Keyword 

Subject 

Rights Statement 

Language 

File Format 

File Extent 

Digitization Specifications 
 Master files scanned at 600 ppi (256 Grayscale) using Capture Perfect 3.0 on a Canon DR9080C in TIF format. PDF derivative scanned at 300 ppi (256 B&W), using Capture Perfect 3.0, on a Canon DR9080C. CVista PdfCompressor 3.1 was used for pdf compression and textual OCR.

Replaces 

Additional Information 
 description.provenance : Approved for entry into archive by Laura Wilson(laura.wilson@oregonstate.edu) on 20071217T17:06:23Z (GMT) No. of bitstreams: 1
Georgieva_Bogdana_A.pdf: 661171 bytes, checksum: 3db50bcb31a933b46d215686820a26f5 (MD5)
 description.provenance : Made available in DSpace on 20071220T23:32:38Z (GMT). No. of bitstreams: 1
Georgieva_Bogdana_A.pdf: 661171 bytes, checksum: 3db50bcb31a933b46d215686820a26f5 (MD5)
 description.provenance : Approved for entry into archive by Laura Wilson(laura.wilson@oregonstate.edu) on 20071220T23:32:38Z (GMT) No. of bitstreams: 1
Georgieva_Bogdana_A.pdf: 661171 bytes, checksum: 3db50bcb31a933b46d215686820a26f5 (MD5)
 description.provenance : Submitted by Anna Opoien (aoscanner@gmail.com) on 20071214T01:07:25Z
No. of bitstreams: 1
Georgieva_Bogdana_A.pdf: 661171 bytes, checksum: 3db50bcb31a933b46d215686820a26f5 (MD5)
