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| A recursive analytical algorithm for dynamics analysis of nonlinear oscillators based on Riemannian geometry |
| Received:January 27, 2018 Revised:October 11, 2018 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20180127001 |
| KeyWord:nonlinear oscillator Riemannian geometry recursive analytic algorithm Runge-Kutta method computational efficiency |
| Author | Institution |
| 杨喆 |
大连理工大学 工程力学系 工业装备结构分析国家重点实验室, 大连, |
| 陈国海 |
大连理工大学 工程力学系 工业装备结构分析国家重点实验室, 大连, |
| 杨迪雄 |
大连理工大学 工程力学系 工业装备结构分析国家重点实验室, 大连, |
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| Abstract: |
| Based on Riemannian geometry and a variational principle,this paper derives the second order differential equation of a nonlinear dissipative dynamical system on the Riemannian manifold.The concept of manifold retraction is applied to discretise the dynamic equation,and the corresponding recursive scheme is established.Three autonomous nonlinear damped oscillator systems are taken as examples,and their differential dynamic equations are solved by using the recursive analytical algorithm and the Runge-Kutta algorithm,respectively.The computational time of the two algorithms with different time steps is also compared.Numerical results indicate in comparison with the Runge-Kutta algorithm,the Riemannian geometry-based recursive algorithm can not only achieve the analytical expression of dynamic equations in each time step,but also its running time is shorter than that of the former with higher computational efficiency.The recursive algorithm for dynamic equations based on Riemannian manifolds offers a new idea for analytically solving nonlinear dynamic systems. |
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