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- [[File:Classical mechanics roadmap.svg|thumb|Variational principles for classical mechanics was developed in parallel with Newtonian mechanics. ...n extremum (minimum, maximum or saddle point) of a function or functional. Variational methods are exploited in many modern software applications to [[Simulation| ...35 KB (4,935 words) - 17:12, 16 June 2025
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- '''Energy principles in structural mechanics''' express the relationships between [[Stress (phys ==General principles== ...3 KB (343 words) - 02:15, 13 December 2020
- {{Short description|Scientific principles enabling the use of the calculus of variations}}{{Inline references needed| ...nary]]—can be solved using [[variational calculus]], and in this case, the variational principle is the following: The solution is a function that minimizes the [ ...5 KB (638 words) - 16:03, 16 June 2025
- ...vity''' refers to various mathematical techniques that employ the use of [[variational calculus]] in [[Albert Einstein|Einstein]]'s theory of [[general relativity *[[Fermat's and energy variation principles in field theory]] ...2 KB (262 words) - 17:46, 30 November 2024
- ...te web|title=Hybrid design methods of cascade profile based on variational principles|url=http://www.emeraldinsight.com/journals.htm?articleid=1502002&show=pdf|w ...ydromechanics,<ref>{{Cite web|title=VARIATIONAL PRINCIPLES AND GENERALIZED VARIATIONAL PRINCIPLE FOR THREE-DIMENSIONAL TRANSONIC FLOW WITH SHOCK WAVES IN A ROTATI ...3 KB (460 words) - 23:52, 27 May 2025
- {{distinguish|text=Schwinger's variational principle, ''[[Schwinger variational principle]]''}} The '''Schwinger's quantum action principle''' is a [[variational method|variational]] approach to [[quantum mechanics]] and [[quantum field theory]].<ref>{{Cit ...4 KB (526 words) - 02:49, 25 May 2025
- | footer = Gauss and Hertz devised variational principles of mechanics The '''principle of least constraint''' is one [[Variational principle|variational formulation]] of [[classical mechanics]] enunciated by [[Carl Friedrich Gau ...8 KB (1,179 words) - 16:26, 24 May 2025
- ...33),<ref>{{cite book|last=Pauli|first=W.|title=Handbuch der Physik|chapter=Principles of Wave Mechanics|volume=24|publisher=Springer|location=Berlin|year=1933|pa ...example finite-order [[Møller–Plesset perturbation theory]], which is not variational.<ref>{{cite book|last=Jensen|first=Frank|title=Introduction to Computationa ...17 KB (2,527 words) - 08:08, 25 May 2025
- ...49)<ref>{{cite journal|author=Lewis, D. C.|title=Review: ''The variational principles of mechanics'', by C. Lanczos|journal=Bull. Amer. Math. Soc.|year=1951|volu * 1949: ''The Variational Principles of Mechanics'' (dedicated to [[Albert Einstein]]), [[University of Toronto ...13 KB (1,766 words) - 19:27, 26 May 2025
- ...r perturbation methods, variational principles and generalized variational principles, finite element methods as well as the measurements of atmospheric electric ...large deflation of circular elastic plates and the generalized variational principles, he won the [[State Natural Science Award]] (Second Class) twice, in 1965 a ...11 KB (1,455 words) - 19:12, 8 June 2025
- ...hysical information concerning the system and the forces acting on it. The variational problem is equivalent to and allows for the derivation of the ''[[different These equations are called the Euler–Lagrange equations for the variational problem. ...16 KB (2,380 words) - 08:09, 9 May 2025
- ...part of geometric analysis, because differential equations arising from [[variational principle]]s have a strong geometric content. Geometric analysis also inclu ...4 KB (605 words) - 01:07, 7 December 2024
- [[File:Classical mechanics roadmap.svg|thumb|Variational principles for classical mechanics was developed in parallel with Newtonian mechanics. ...n extremum (minimum, maximum or saddle point) of a function or functional. Variational methods are exploited in many modern software applications to [[Simulation| ...35 KB (4,935 words) - 17:12, 16 June 2025
- ...nczos>{{cite book|last=Lanczos|first=Cornelius|date=1964|title=Variational principles of mechanics|url=https://archive.org/details/variationalprinc00lanc/page/92 ...=2018 |title=From Lagrangian Mechanics to Nonequilibrium Thermodynamics: A Variational Perspective |journal=Entropy |language=en |volume=21 |issue=1 |pages=8 |doi ...16 KB (2,503 words) - 01:41, 24 June 2025
- .....44..146N |issn=0031-921X|url-access=subscription }}</ref> Action and the variational principle are used in [[Path integral formulation|Feynman's formulation of {{Main | History of variational principles in physics}} ...23 KB (3,410 words) - 23:35, 19 June 2025
- ...raphs) on mathematics. Fomenko is a specialist in geometry and topology, [[variational calculus]], [[symplectic topology]], [[Hamiltonian mechanics|Hamiltonian ge ...en, Fred|author-link=Frederick J. Almgren, Jr.|title=Review: ''Variational principles of topology''|journal=Bull. Amer. Math. Soc. (N.S.)|year=1992|volume=26|iss ...17 KB (2,274 words) - 15:23, 16 June 2025
- ...f deformable bodies.<ref>Dym, C. L. and I. H. Shames, ''Solid Mechanics: A Variational Approach'', McGraw-Hill, 1973.</ref> ...d is commonly considered as the prototype of the contemporary virtual work principles.<ref name=capecchi/> In 1743 D'Alembert published his ''Traité de Dynamique ...45 KB (7,351 words) - 20:57, 27 May 2025
- ...nal principles, for example the [[Schwinger-Lanczos method]] combining the variational principle of [[Julian Schwinger|Schwinger]] with [[Lanczos algorithm]]. ...last2=Schwinger|first2=J.|author-link2=Julian Schwinger| title=Variational Principles for Scattering Processes. I|journal=Phys. Rev. Lett.|year=1950|volume=79|is ...17 KB (2,584 words) - 03:11, 13 February 2025
- ...]]. A differential equation describing their shape may be derived, using [[variational principle]]s, by minimizing (or finding the extremum) of the [[energy]] of ...6 KB (1,004 words) - 06:21, 14 April 2025
- * David Bleecker, ''Gauge Theory and Variational Principles'', Addison-Wesley publishing, Reading, Mass (1981). {{ISBN|0-201-10096-7}}. ...8 KB (1,267 words) - 17:28, 20 November 2024
- ...nlinear techniques are roughly classified into analytical, topological and variational methods. Mark Krasnoselsky has contributed to all three aspects in a signif ...e suggested a new general method for investigating degenerate extremals in variational problems and developed qualitative methods for studying critical and bifurc ...12 KB (1,571 words) - 10:25, 10 May 2025