2011/03/08 by Tianshu Luo, Luo, Tianshu, Yimu Guo +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1103.1455
arxiv created 2011/03/08 · arxiv updated 2011/03/09
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 qi 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.