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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

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
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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
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