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  • 1
    Electronic Resource
    Electronic Resource
    Separability structures corresponding to conservative dynamical systems (1984)
    Springer
    Meccanica 19 (1984), S. 275-281 
    Details
    ISSN: 1572-9648
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Summary We discuss a method of integration of the Hamilton-Jacobi equation corresponding to a quadratic Hamiltonian with a potential function and satisfying the Levi-Civita separability conditions. We prove the existence of suitable coordinates (called normal separable coordinates) by direct construction and we establish the general form of the Hamilton-Jacobi equation in such coordinates.
    Notes: Sommario Si presenta un metodo di integrazione delle equazioni di Hamilton-Jacobi che corrispondono ad una hamiltoniana quadratica con potenziale e che soddisfano le condizioni di separabilità secondo Levi-Civita. Si dimostra in modo costruttivo l'esistenza di opportuni sistemi di coordinate (dette coordinate separabili normali) e si determina la forma generale dell'equazione di Hamilton-Jacobi in tali coordinate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01556323
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  • 2
    Electronic Resource
    Electronic Resource
    Derivations of differential forms on jet bundles (1987)
    Springer
    Annali di matematica pura ed applicata 147 (1987), S. 249-265 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Résumé On présente une généralization de la théorie des dérivations des formes extérieures, formulée par Frölicher et Nijenhuis [2], au cas des dérivations qui relient les formes extérieurs sur deux variétés différentes. On utilize ensuite cette théorie généralizée pour étudier les dérivations des limites directes des algèbres des formes extérieures sur les fibrés des jets. Ces dérivations ont été appliquées dans l'analyse des équations de Lie [3], [4] et dans le problème inverse du calcul des variations [6], [7], [8], [9].
    Notes: Summary The theory of derivations of differential forms, originally formulated by Frölicher and Nijenhuis [2], is generalized to include derivations which connect differential forms on two different manifolds. This generalized theory is then used to analyze derivations of direct limits of exterior algebras of forms on jet bundles. Such derivations have found applications in the analysis of Lie equations [3], [4] and in the inverse problem of the calculus of variations [6], [7], [8], [9].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01762420
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