ON A GEOMETRIC FRAMEWORK FOR LAGRANGIAN SUPERMECHANICS

被引：2
|
作者：
Bruce, Andrew James [1 ]
Grabowska, Katarzyna [2 ]
Moreno, Giovanni [3 ]
机构：
[1] Univ Luxembourg, Math Res Unit, Maison Nombre 6,Ave Fonte, L-4364 Esch Sur Alzette, Luxembourg
[2] Univ Warsaw, Fac Phys, Pasteura 5, PL-02093 Warsaw, Poland
[3] Polish Acad Sci, Inst Math, Ul Sniadeckich 8, PL-00656 Warsaw, Poland
来源：
JOURNAL OF GEOMETRIC MECHANICS | 2017年 / 9卷 / 04期
关键词：
Supermechanics; supermanifolds; Lagrangian systems; Tulczyjew triples; curves; SYMMETRIES; MECHANICS; DYNAMICS;
D O I：
10.3934/jgm.2017016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We re-examine classical mechanics with both commuting and anticommuting degrees of freedom. We do this by defining the phase dynamics of a general Lagrangian system as an implicit differential equation in the spirit of Tulczyjew. Rather than parametrising our basic degrees of freedom by a specified Grassmann algebra, we use arbitrary supermanifolds by following the categorical approach to supermanifolds.
引用
收藏
页码：411 / 437
页数：27
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