First integrals via polynomial canonical transformations
Copyright policy )First integrals via polynomial canonical transformations
Maharatna, Dutt, and Chattarji [J. Math. Phys. 20, 2221 (1979)] discussed the use of time-dependent canonical transformations for the determination of first integrals for time-dependent Hamiltonian systems. One particular proposal that successive time-dependent polynomial canonical transformations will enable first integrals to be found for a wider variety of time-dependent polynomial Hamiltonians than can be obtained using time-dependent linear canonical transformations is shown to be not true for the paradigm which they selected. It is suggested that their ansatz is ill-founded in general.
- University of the Witwatersrand South Africa
Hamilton's equations, time-dependent polynomial Hamiltonians, time-dependent polynomial canonical transformations, Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics, Hamilton-Jacobi equations in mechanics, generalization of damped Duffing oscillator, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
Hamilton's equations, time-dependent polynomial Hamiltonians, time-dependent polynomial canonical transformations, Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics, Hamilton-Jacobi equations in mechanics, generalization of damped Duffing oscillator, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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