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We have already encountered the Newtonian, Euler-Lagrange, Hamiltonian and Poisson bracket formulations of (nonrelativistic) mechanics. In this chapter, we place mechanical systems in the framework of dynamical systems by viewing them in terms of vector fields Vector fields in the differential geometric setting of manifolds and tensor fields and their behavior under changes of coordinates are discussed in Appendix B.

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Dynamics Viewed as a Vector Field on State Space

  • 章节

  • 发表日期：

    2025年

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  • Govind S. Krishnaswami

摘要

We have already encountered the Newtonian, Euler-Lagrange, Hamiltonian and Poisson bracket formulations of (nonrelativistic) mechanics. In this chapter, we place mechanical systems in the framework of dynamical systems by viewing them in terms of vector fields Vector fields in the differential geometric setting of manifolds and tensor fields and their behavior under changes of coordinates are discussed in Appendix B.