Abstract
In this work, we apply the geometric Hamilton-Jacobi theory to obtain solution of Hamiltonian systems in classical mechanics that are either compatible with two structures: the first structure plays a central role in the theory of time- dependent Hamiltonians, whilst the second is used to treat classical Hamiltonians including dissipation terms. It is proved that the generalization of problems from the calculus of variation methods in the nonstationary case can be obtained naturally in Hamilton-Jacobi formalism.
Highlights
Since Bateman proposed the time-dependent Hamiltonian in a classical context[1] for the illustration of dissipative systems, there has been much attention paid to quantum-mechanical treatments of nonlinear and non conservative systems
Hamilton Jacobi equations (HJE) are nonlinear first order equations which have been first introduced in classical mechanics, butfind applications in many other fields of mathematics
We have derived an expression for the Hamilton-Jacobi equation and have applied our results for a number of time-dependent models including dissipation terms
Summary
Since Bateman proposed the time-dependent Hamiltonian in a classical context[1] for the illustration of dissipative systems, there has been much attention paid to quantum-mechanical treatments of nonlinear and non conservative systems. Hamilton Jacobi equations (HJE) are nonlinear first order equations which have been first introduced in classical mechanics, butfind applications in many other fields of mathematics. Hamilton-Jacobi method has been studied for a wide range of systems with time-independent For systems with time-dependent Hamiltonians, due to the complexity of dynamics, little has been known about quantum of action variables.
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