Geodesic
Trace formula in Lagrangian mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 52-63 Cet article a éte moissonné depuis la source Math-Net.Ru

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The variational equation (Jacobi equation) on a fixed trajectory of a natural Lagrangian system leads to a certain linear differential operator. The trace formula expresses a suitably regularized determinant of this operator in terms of the determinant of a finite-dimensional operator generated by the classical motion in the neighborhood of the trajectory. The aim of the paper is to discuss such a formula in a fairly free geometrical framework and establish its connection with the trace formula in general Hamiltonian mechanics, which was the subject of a preceding publication of the authors. 
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     author = {V. S. Buslaev and E. A. Nalimova},
     title = {Trace formula in {Lagrangian} mechanics},
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}
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V. S. Buslaev; E. A. Nalimova. Trace formula in Lagrangian mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 52-63. http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a5/

[1] Buslaev V. S., Nalimova E. A., TMF, 60:3 (1984), 344–355 | MR | Zbl

[2] Buslaev V. S., DAN SSSR, 182:4 (1968), 743–746 | MR | Zbl

[3] Besse A., Mnogoobraziya s zamknutymi geodezicheskimi, Mir, M., 1981, 327 pp. | MR