Time-dependent contact mechanics

被引：18

作者：

de Leon, Manuel ^{[1
]}

Gaset, Jordi ^{[2
]}

Gracia, Xavier ^{[3
]}

Munoz-Lecanda, Miguel C. ^{[3
]}

Rivas, Xavier ^{[2
]}

机构：

[1] Consejo Super Invest Cient & Real Acad Ciencias, Inst Ciencias Matemat, Madrid, Spain

[2] Univ Int La Rioja, Escuela Super Ingn & Tecnol, Logrono, Spain

[3] Univ Politecn Cataluna, Dept Math, Barcelona, Spain

来源：

MONATSHEFTE FUR MATHEMATIK | 2023年 / 201卷 / 04期

关键词：

Contact structure; Time-dependent system; Hamiltonian system; Dissipation; Singular Lagrangian; Holonomic constraints; Jacobi structure; LAGRANGIAN SYSTEMS; GEOMETRIC ASPECTS;

D O I：

10.1007/s00605-022-01767-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Contact geometry allows us to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact systems: cocontact manifolds. Within this setting we develop the Hamiltonian and Lagrangian formalisms, both in the regular and singular cases. In the singular case, we present a constraint algorithm aiming to find a submanifold where solutions exist. As a particular case we study contact systems with holonomic time-dependent constraints. Some regular and singular examples are analyzed, along with numerical simulations.

引用

页码：1149 / 1183

页数：35

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