Annali di Matematica Pura ed Applicata

, Volume 35, Issue 1, pp 183–202 | Cite as

The scalar form of Jacobi's equations in the calculus of variations

  • Hanno Rund


The tensorial equations of geodesic deviation in a generalised metric (Finsler) space of n dimensions are reduced to a single equation in scalar form involving only the length of the infinitesimal variation vector. The terms occurring in this equation are interpreted geometrically by means of the theory of subspaces. An expression for the second variation of the length integral is determined, from which the differential equations of the accessory problems are obtained. These, the so-calledJacobi equations, are shown to contain the above-mentioned scalar form of the equation of geodesic deviation as a special case. This leads to a novel general discussion of the accessory problem in Calculus of Variations.


Differential Equation Single Equation Scalar Form Variation Vector Accessory Problem 
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Copyright information

© Swets & Zeitlinger B. V. 1953

Authors and Affiliations

  • Hanno Rund
    • 1
  1. 1.BonnGermany

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