Open AccessThe conserved quantities in general theorems ofthe Cosserat elastic rod dynamics
Author(s) -
Yun Xiao,
Peng Wang
Publication year - 2011
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.60.114501
Subject(s) - conserved quantity , conservation law , momentum (technical analysis) , arc (geometry) , classical mechanics , conservation of energy , energy–momentum relation , coordinate system , angular momentum , moment (physics) , dynamics (music) , physics , mathematics , mathematical analysis , geometry , quantum mechanics , finance , acoustics , economics
Conserved quantities of the Cosserat elastic rod dynamics are studied according to the general theorems of dynamics. The rod dynamical equation takes the cross section of the rod as its objective of study and is expressed by two independent variables, the arc coordinate of the rod and the time, so the conserved quantities are written in the integral forms and there exist the arc coordinate conservation and the time conservation. The existence conditions and the formulas of conservations of momentum and moment of momentum are derived from the theorem of momentum and the theorem of moment of momentum respectively, which contain two cases of conserved quanties, one is the time and the other is arc coordinate. Also existence conditions and formulas of conservations of energy about time and are coordinate, which contain mechanical energy conservation, are derived from energy equations about the time and arc coordinate of the rod respectively. All of conservative motions of the rod are explained by examples. The conserved quantities in the integral form are of practical significance in both theoretical and numerical analysis for the Cosserat elastic rod dynamics.