Invariante Variationsprobleme [chapter]

Emmy Noether
1983 Springer Collected Works in Mathematics  
The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in Section 1 and proved in following sections. Concerning these differential equations that arise from problems of variation, far more precise statements can be made than about arbitrary differential equations admitting of a group, which are the subject of Lie's
more » ... subject of Lie's researches. What is to follow, therefore, represents a combination of the methods of the formal calculus of variations with those of Lie's group theory. For special groups and problems in variation, this combination of methods is not new; I may cite Hamel and Herglotz for special finite groups, Lorentz and his pupils (for instance Fokker), Weyl and Klein for special infinite groups. 1 Especially Klein's second Note and the present developments have been mutually influenced by each other, in which regard I may refer to the concluding remarks of Klein's Note. 0 This paper is reproduced by Frank Y. Wang ( with L A T E X.
doi:10.1007/978-3-642-39990-9_13 fatcat:auiizmn6crb7jhe5cmrb76hzpe