NDLI: Noether symmetries of the nonconservative and nonholonomic systems on time scales

Content Provider	Springer Nature Link
Author	Cai, PingPing Fu, JingLi Guo, YongXin
Copyright Year	2013
Abstract	In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales $$\mathbb{T}$$ , which unifies the Noether’s theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton’s principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether’s theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d’Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether’s theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether’s theorems for discrete systems. Several examples are given to illustrate the application of our results.
Starting Page	1017
Ending Page	1028
Page Count	12
File Format	PDF
ISSN	16747348
Journal	Science in China Series G
Volume Number	56
Issue Number	5
e-ISSN	18691927
Language	English
Publisher	SP Science China Press
Publisher Date	2013-04-19
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	time scale Lagrange equation delta derivative Noether’s theorem nonconservative and nonholonomic system Physics Classical Continuum Physics Astronomy, Observations and Techniques
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Noether-type theorem for discrete nonconservative dynamical systems with nonregular lattices

Nonconservative mechanical systems with nonholonomic constraints

Symmetries and exact solutions of discrete nonconservative systems

Non-Noether symmetries and Lutzky conservative quantities of nonholonomic nonconservative dynamical systems

Velocity-dependent symmetries and non-Noether conserved quantities of electromechanical systems

Noether-type theory for discrete mechanico-electrical dynamical systems with nonregular lattices

Symmetries for Nonconservative Field Theories on Time Scale

Bridging length and time scales in moving contact line problems

Tensor coupling effect on relativistic symmetries

Noether symmetries of the nonconservative and nonholonomic systems on time scales

Similar Documents

Noether-type theorem for discrete nonconservative dynamical systems with nonregular lattices

Nonconservative mechanical systems with nonholonomic constraints

Symmetries and exact solutions of discrete nonconservative systems

Non-Noether symmetries and Lutzky conservative quantities of nonholonomic nonconservative dynamical systems

Velocity-dependent symmetries and non-Noether conserved quantities of electromechanical systems

Noether-type theory for discrete mechanico-electrical dynamical systems with nonregular lattices

Symmetries for Nonconservative Field Theories on Time Scale

Bridging length and time scales in moving contact line problems

Tensor coupling effect on relativistic symmetries

Noether symmetries of the nonconservative and nonholonomic systems on time scales