Open AccessOn d-δ commutation relation of constrained differential systems
Author(s) -
YongXin Guo,
Zhe Zhao,
Shixing Liu,
Chang Liu
Publication year - 2008
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.57.1301
Subject(s) - commutation , relation (database) , differential (mechanical device) , differential operator , affine transformation , mathematics , algebraic differential equation , operator (biology) , computer science , differential equation , mathematical analysis , pure mathematics , ordinary differential equation , physics , differential algebraic equation , quantum mechanics , voltage , biochemistry , chemistry , repressor , database , transcription factor , gene , thermodynamics
An important problem of calculus of variations used in constrained differential systems, i.e., the commutation relation of differential operator and variational oprerator, is investigated by means of Frobenius theorem of integrability. Based on analyzing the d-δ commutation relation for the linear stationay differential constrained systems and affine differential constrained systems, the relationship between noncommutator of differentiation and variation and nonholonomicity of the differential constraints is briefly proved by means of Frobenius integrability theory. The commutation relation for non-linear differential constrained systems is also discussed in the paper. Finally, three examples are given to verify the results.