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Über die kanonischen Veränderlichen in der Variationsrechnung der mehrfachen Integrale

In: Festschrift

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  • C. Carathéodory

Abstract

Zusammenfassung Man ist bisher der Meinung gewesen, daß die gewöhnliche Legendresche Transformation auch in der Variationsrechnung der mehrfachen Integrale Koordinaten liefert, die den von Hamilton entdeckten kanonischen Veränderlichen der Variationsrechnung der Linienintegrale entsprechen 1). Dies ist aber, wie aus den folgenden Überlegungen ersichtlich, nicht der Fall: statt der Legendreschen Transformation kommt hier eine Verallgemeinerung derselben in Betracht, welche von der Mehrfachheit, μ des betrachteten Integrals abhängt, und nur für, μ = 1 mit der ersten zusamm3nfällt.

Suggested Citation

  • C. Carathéodory, 1982. "Über die kanonischen Veränderlichen in der Variationsrechnung der mehrfachen Integrale," Springer Books, in: Festschrift, pages 78-88, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-61810-9_11
    DOI: 10.1007/978-3-642-61810-9_11
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