Buslaev, V. S.; Nalimova, E. A. Trace formula in Lagrangian mechanics. (English. Russian original) Zbl 0598.70023 Theor. Math. Phys. 61, 989-997 (1984); translation from Teor. Mat. Fiz. 61, No. 1, 52-63 (1984). (From the authors’ summary.) 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 neighbourhood of the trajectory. The aim of the paper is to discuss such a formula in a fairly free geometrical frame work and to establish its connection with the trace formula in general Hamiltonian mechanics. Reviewer: P.Smith Cited in 2 Documents MSC: 70H03 Lagrange’s equations 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 49J15 Existence theories for optimal control problems involving ordinary differential equations Keywords:variational equation; Jacobi equation; fixed trajectory; natural Lagrangian system; trace formula; regularized determinant; finite- dimensional operator; classical motion PDF BibTeX XML Cite \textit{V. S. Buslaev} and \textit{E. A. Nalimova}, Theor. Math. Phys. 61, 989--997 (1984; Zbl 0598.70023); translation from Teor. Mat. Fiz. 61, No. 1, 52--63 (1984) Full Text: DOI OpenURL References: [1] V. S. Buslaev and E. A. Nalimova, Teor. Mat. Fiz.,60, 344 (1984). [2] V. S. Buslaev, Dokl. Akad. Nauk SSSR,182, 743, (1968). [3] A. L. Besse, Manifolds all of whose Geodesics are Closed, Berlin (1978). · Zbl 0387.53010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.