Unconventional Hamilton-type variational principle in phase space and symplectic algorithm.

Luo, En; Huang, Weijiang; Zhang, Johnson

Abstract

By a novel approach proposed by Luo, the unconventional Hamilton-type variational principle in phase space for elastodynamics of multidegree-of-freedom system is established in this paper. It not only can fully characterize the initial-value problem of this dynamic, but also has a natural symplectic structure. Based on this variational principle, a symplectic algorithm which is called a symplectic time-subdomain method is proposed. A non-difference scheme is constructed by applying Lagrange interpolation polynomial to the time subdomain. Furthermore, it is also proved that the presented symplectic algorithm is an unconditionally stable one. From the results of the two numerical examples of different types, it can be seen that the accuracy and the computational efficiency of the new method excel obviously those of widely used Wilson-? and Newmark-? methods. Therefore, this new algorithm is a highly efficient one with better computational performance.

Citation

Luo, E., Huang, W., & Zhang, J. (2003). Unconventional Hamilton-type variational principle in phase space and symplectic algorithm. SCIENCE CHINA Physics, Mechanics and Astronomy, 46, 248-258. https://doi.org/10.1360/03yg9033

• Journal Article Type: Article
• Publication Date: Jun 1, 2003
• Deposit Date: Jun 13, 2008
• Print ISSN: 1674-7348
• Electronic ISSN: 1869-1927
• Publisher: BMC
• Peer Reviewed: Peer Reviewed
• Volume: 46
• Pages: 248-258
• DOI: https://doi.org/10.1360/03yg9033
• Keywords: Hamilton-type; varaitional principle; phase space; elastodynamics; symplectic algorithm; symplectic time-subdomain
• Public URL: http://researchrepository.napier.ac.uk/id/eprint/1942