Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm
نویسندگان
چکیده
We propose the difference discrete variational principle in discrete mechanics and symplectic algorithm with variable step-length of time in finite duration based upon a noncommutative differential calculus established in this paper. This approach keeps both symplicticity and energy conservation discretely. We show that there exists the discrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existence in finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodic perturbation. The numerical results are satisfactory. ∗Email: [email protected] †Email: [email protected] , [email protected] ‡Email: [email protected]
منابع مشابه
Difference Discrete Variational Principle , Euler - Lagrange Cohomology and Symplectic , Multisymplectic Structures
We study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncomutative differential geometry. By virtue of this variational principle, we get the difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical ...
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