English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

When a set of particles are moving in a potential field, two aspects areconcerned: 1) the relative motion of particle in spatial domain; 2) theparticle velocity variations in time domain. The difficulty on treating thesystems is originated from the fact that the motion in time domain and themotion in spatial domain are coupled together completely. Generally, for aHamilton dynamic system established by a set of general velocity functions,several abstract theories have been well established, such as Lie algebra,Symplectic manifold, Poisson brackets, and others. However, mathematically, tofind out a general Hamilton function is very difficult even for very simpleproblems. Inspired by these abstract mathematic researches, the Hamiltondynamic system is studied by geometrical field theory of deformation. Firstly,referring to the instant configuration, the deformation tensor in spatialdomain and the velocity transformation tensor in time domain are establishedfor a dynamic system defined by a set of general velocity functions. Secondly,the general deformation tensor in velocity space domain is obtained. Fromcontinuum mechanics point, the stress tensor is defined through introducingbackground feature of space. Then, the general motion equations areestablished. Based on them, the simple motions are divided into two classes: 1)stable motion; and 2) radiating motion. Both of them have quantum solutionstructures. The features of space-time continuum are studied to obtain someintrinsic understanding about basic physical facts. This research shows anengineering way to treat the Hamilton dynamic system.

Geometrical Field Theory of Hamilton Dynamic System In Rational Mechanics