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In the first part of this chapter, the formalism developed in Chap. 2 is reformulated from the standpoint of variational principles: the usual variational method which is familiar in the conventional Hamiltonian dynamics is generalized such that the space of infinitesimal variations is extended to functional spaces in higher dimensions. In the second part, a generalized Hamilton-Jacobi theory of Nambu dynamics is given with some concrete examples.

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The Extension of Variational Principle and Hamilton–Jacobi Theory to Nambu Dynamics

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  • 发表日期：

    2026年

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  • Tamiaki Yoneya

摘要

In the first part of this chapter, the formalism developed in Chap. 2 is reformulated from the standpoint of variational principles: the usual variational method which is familiar in the conventional Hamiltonian dynamics is generalized such that the space of infinitesimal variations is extended to functional spaces in higher dimensions. In the second part, a generalized Hamilton-Jacobi theory of Nambu dynamics is given with some concrete examples.