Trace formula in Lagrangian mechanics (Q1079968)
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scientific article; zbMATH DE number 3965496
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Trace formula in Lagrangian mechanics |
scientific article; zbMATH DE number 3965496 |
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Trace formula in Lagrangian mechanics (English)
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1984
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(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.
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variational equation
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Jacobi equation
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fixed trajectory
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natural Lagrangian system
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trace formula
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regularized determinant
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finite- dimensional operator
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classical motion
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