Canonical transformations and exact invariants for time-dependent Hamiltonian systems (Q2783439)
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scientific article; zbMATH DE number 1730223
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Canonical transformations and exact invariants for time-dependent Hamiltonian systems |
scientific article; zbMATH DE number 1730223 |
Statements
16 November 2003
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time-dependent potentials
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exact invariants
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Hamiltonain systems
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infinitesimal canonical transformation
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extended phase-space
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integral of energy balance equation
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time-dependent damped oscillator
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time-dependent undamped oscillator
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Canonical transformations and exact invariants for time-dependent Hamiltonian systems (English)
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The aim is to present a method in order to obtain exact invariants for non-relativistic Hamiltonian systems with general time-dependent potentials. The main tool is an infinitesimal canonical transformation of the extended phase space. For a specific class of Hamiltonian systems, the exact invariant is obtained equivalently performing in the extended phase space a finite canonical transformation of the initially time-dependent Hamiltonian to a time-independent one. It is furthermore shown that the invariant can be expressed as an integral of energy balance equation. More concretely, three examples of time-dependent damped and undamped oscilators are detailed.
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