Lobe area in adiabatic Hamiltonian systems

Conference · Mon Jan 01 04:00:00 EST 1990

DOI:https://doi.org/10.1016/0167-2789(91)90233-Y· OSTI ID:6648916

Kaper, T J; Wiggins, S ^[1]

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1. California Inst. of Tech., Pasadena, CA (USA) Los Alamos National Lab., NM (USA). Center for Nonlinear Studies

We establish as analytically computable formula, based on the adiabatic Melnikov function, for lobe area in one-degree-of-freedom Hamiltonian systems depending on a parameter which varies slowly in time. We illustrate this lobe area result on a slowly parametrically forced pendulum, a paradigm problem for adiabatic chaos. Our analysis unties the theory of action from classical mechanics with the theory of the adiabatic Melnikov function from the field of global bifurcation theory.

• Research Organization: Los Alamos National Lab., NM (USA)
• Sponsoring Organization: DOD; DOE/AD; NSF
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 6648916
• Report Number(s): LA-UR-90-2714; CONF-9005237--6; ON: DE90016566; CNN: DPP 8968
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ANALYTICAL SOLUTION
HAMILTONIANS
MATHEMATICAL OPERATORS
NONLINEAR PROBLEMS
ORBITS
PENDULUMS
QUANTUM OPERATORS