{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:41:41Z","timestamp":1777902101405,"version":"3.51.4"},"reference-count":23,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2006,4,1]],"date-time":"2006-04-01T00:00:00Z","timestamp":1143849600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIMULATION"],"published-print":{"date-parts":[[2006,4]]},"abstract":"<jats:p>The purpose of this article is to obtain conservation laws (invariants of motion) for different energy domains through the extended Noether theorem and bond graphs. Bond graphs are profitably used in representing the physics of a system as well as obtaining its umbra-Lagrangian. The article extends Lagrangian-Hamiltonian mechanics to deal with asymmetries in the system, which incorporates dissipative and nonpotential fields in a compact Lagrangian form, such that one may obtain invariants of motion through extension of Noether\u2019s theorem. A detailed methodology is outlined in this article for obtaining the invariants of motion for a general class of asymmetric systems with a gauge-transformed umbra-Lagrangian. Symmetrization of an asymmetric system is introduced through the concept of gauge functions, for which the classical Noether theorem is extended over vector fields in the extended manifold comprising real and umbra displacements and velocities, as well as real time. A generalization of the variational principle or least action principle is also presented, which leads to the proposed form of the umbra-Lagrange equation through recursive minimization of functionals. Several illustrative examples are given to elucidate this concept in different physical contexts.<\/jats:p>","DOI":"10.1177\/0037549706068285","type":"journal-article","created":{"date-parts":[[2006,8,7]],"date-time":"2006-08-07T07:31:13Z","timestamp":1154935873000},"page":"207-226","source":"Crossref","is-referenced-by-count":9,"title":["A Methodology for Finding Invariants of Motion for Asymmetric Systems with                 Gauge-Transformed Umbra Lagrangian Generated by Bond Graphs"],"prefix":"10.1177","volume":"82","author":[{"given":"Amalendu","family":"Mukherjee","sequence":"first","affiliation":[{"name":"Mechanical Engineering Department Indian Institute of Technology 721302                         Kharagpur, India,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vikas","family":"Rastogi","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Department Sant Longowal Institute of Engineering                         and Technology Longowal, 148106, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anirvan","family":"Dasgupta","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Department Indian Institute of Technology 721302                         Kharagpur, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2006,4,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.5479\/sil.322586.39088000898585"},{"key":"atypb2","volume-title":"Lectures in analytical mechanics","author":"Gantmachar, F.","year":"1970"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7462(70)90024-7"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7462(78)90007-0"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7462(73)90039-5"},{"key":"atypb6","first-page":"661","volume-title":"Proceedings of CISS\u20141st Conference of International Simulation Societies","author":"Mukherjee, A."},{"key":"atypb7","volume-title":"Analysis and simulation of multiport systems: The bondgraph approach to physical system dynamics","author":"Karnopp, D. 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Ph.D. diss., Indian Institute of Technology,                 Kharagpur, India."}],"container-title":["SIMULATION"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549706068285","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549706068285","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T11:19:43Z","timestamp":1777634383000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0037549706068285"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,4]]}},"alternative-id":["10.1177\/0037549706068285"],"URL":"https:\/\/doi.org\/10.1177\/0037549706068285","relation":{},"ISSN":["0037-5497","1741-3133"],"issn-type":[{"value":"0037-5497","type":"print"},{"value":"1741-3133","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,4]]}}}