Physics – Mathematical Physics
Scientific paper
2011-03-08
Physics
Mathematical Physics
Scientific paper
In this paper an approach is outlined. With this approach some explicit algorithms can be applied to solve the initial value problem of $n-$dimensional damped oscillators. This approach is based upon following structure: for any non-conservative classical mechanical system and arbitrary initial conditions, there exists a conservative system; both systems share one and only one common phase curve; and, the value of the Hamiltonian of the conservative system is, up to an additive constant, equal to the total energy of the non-conservative system on the aforementioned phase curve, the constant depending on the initial conditions. A key way applying explicit symplectic algorithms to damping oscillators is that by the Newton-Laplace principle the nonconservative force can be reasonably assumed to be equal to a function of a component of generalized coordinates $q_i$ along a phase curve, such that the damping force can be represented as a function analogous to an elastic restoring force numerically in advance. Two numerical examples are given to demonstrate the good characteristics of the algorithms.
Guo Yimu
Luo Tianshu
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