Abstract
Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kähler manifolds, and the Hamiltonian mechanics on Kähler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton’s equations was obtained, and so on.
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References
Gantmaher F R. Lecture of Analytical Mechanics[M]. Zhong Fenge, Xue Weixi (transls). People’s Education Press, Beijing, 1963, 1–163 (in Chinese).
Arnold V I. Mathematical Methods of Classical Mechanics[M]. Springer-Verlag, New York, 1978, 1–300.
Arnold V I. Mathematical Aspect of Classical and Celestial Mechanics[M]. Encyclopedial of Mathematical Sciences, Vol.3. Dynamical Systems III. Spiringer-Verlag, New York, Berlin Heideberg, 1985, 1–48.
Curtis W D, Miller F R. Differential Manifolds and Theoretical Physics[M]. Academic Press Inc, Orlando, Florida, 1985, 1–191.
Dubrovin B A, Fomenko A T, Novikov S P. Modern Geomery—Methods and Application, Part I, Part II[M]. Springer-Verlag Inc, New York, 1984, I: 1–374, II: 1–357.
von Westenhoz C. Differential Forms in Mathematical Physics[M]. North-Holland Publishing Company, Amsterdam, New York, Oxford, 1978, 335–439.
Zhang Rongye. Newtonian mechanics on Kähler manifold[J]. Applied Mathematics and Mechanics (English Edition), 1996, 17(8):751–764.
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Communicated by ZHOU Zhe-wei
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Zhang, Ry. Hamiltonian mechanics on Kähler manifolds. Appl Math Mech 27, 353–362 (2006). https://doi.org/10.1007/s10483-006-0311-z
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DOI: https://doi.org/10.1007/s10483-006-0311-z