Abstract A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler--Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.
Received: 06 February 2008
Revised: 08 April 2008
Accepted manuscript online:
PACS:
84.30.Bv
(Circuit theory)
Fund: Project supported by the National
Natural Science Foundation of China (Grant Nos 10672143 and
60575055) and the State Key Laboratory of Scientific and Engineering
Computing, Chinese Academy of Sciences and the Natural Science
Foundation of Henan Province Government, China (Grant No
0511022200).
Cite this article:
Fu Jing-Li (傅景礼), Chen Ben-Yong (陈本永), Tang Yi-Fa(唐贻发), Fu Hao(付昊) Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems 2008 Chin. Phys. B 17 3942
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