Statics in the momentum current picture
作者:
F. Herrmann,
G. Bruno Schmid,
期刊:
American Journal of Physics
(AIP Available online 1984)
卷期:
Volume 52,
issue 2
页码: 146-152
ISSN:0002-9505
年代: 1984
DOI:10.1119/1.13923
出版商: American Association of Physics Teachers
关键词: forces;continuum mechanics;elasticity;stresses;static problems;linear momentum;continuity equations;structural beams
数据来源: AIP
摘要:
Newton’s Second Law is equivalent to the continuity equation for momentum in integral form. This insight leads to an alternative picture of forces as momentum currents. The purpose of the present paper is to introduce a new approach to statics problems and their solutions in terms of momentum currents. In particular, the relation between the distribution of momentum currents and the elastic stresses within a medium will be considered and a simple way to pictorially represent those stresses with the help of momentum flow diagrams will be discussed. Handling statics problems in the momentum current picture immediately displays their relationship to analogous problems in electrical network theory. This uncovers a structural relationship between the role of electric charge in the theory of electricity and the role of momentum in mechanics. For example, it will be shown that the familiar method for the solution of statics problems in terms of free‐body diagrams is equivalent to the use of a junction rule for momentum currents.
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