Editing D'Alembert's principle (section)

{{distinguish|text = [[d'Alembert's equation]] or the [[d'Alembert operator]]}}
{{short description|Statement in classical mechanics}}
[[File:Alembert d' – Traité de dynamique, 1743 – BEIC 15685.jpg|thumb|''Traité de dynamique'' by [[Jean Le Rond d'Alembert]], 1743. In it, the French scholar enunciated the principle of the quantity of movement, also known as "D'Alembert's principle".]]
{{Classical mechanics|cTopic=Fundamental concepts}}
[[Image:Alembert.jpg|thumb|right|[[Jean d'Alembert]] (1717–1783)]]

'''D'Alembert's principle''', also known as the '''Lagrange–d'Alembert principle''', is a statement of the fundamental [[classical physics|classical]] laws of motion. It is named after its discoverer, the French physicist and mathematician [[Jean le Rond d'Alembert]], and Italian-French mathematician [[Joseph Louis Lagrange]]. D'Alembert's principle generalizes the [[principle of virtual work]] from [[statics|static]] to [[dynamical system]]s by introducing ''forces of inertia'' which, when added to the applied forces in a system, result in ''dynamic equilibrium''.<ref name=Lanczos>{{cite book|last=Lanczos|first=Cornelius|date=1964|title=Variational principles of mechanics|url=https://archive.org/details/variationalprinc00lanc/page/92/mode/2up|page=92|publisher=Toronto, University of Toronto Press }}</ref><ref>{{cite book|last=d'Alembert|first=Jean le Rond|date=1743|title=Traité de dynamique|url=https://books.google.com/books?id=XrEWAAAAQAAJ|pages=50–51}}</ref>

D'Alembert's principle can be applied in cases of [[nonholonomic constraint |kinematic constraints]] that depend on velocities.<ref name=Lanczos/>{{rp|92}} The principle does not apply for irreversible displacements, such as sliding [[friction]], and more general specification of the irreversibility is required.<ref>{{cite journal | last1 = Udwadia | first1 = F. E. | last2 = Kalaba | first2 = R. E. | title = On the Foundations of Analytical Dynamics | journal = Intl. Journ. Nonlinear Mechanics | volume = 37 | issue = 6 | pages = 1079–1090 | date = 2002 | url = http://ae-www.usc.edu/bio/udwadia/papers/On_foundation_of_analytical_dynamics.pdf | doi = 10.1016/S0020-7462(01)00033-6 | bibcode = 2002IJNLM..37.1079U | url-status = dead | archive-url = https://web.archive.org/web/20100613031338/http://ae-www.usc.edu/bio/udwadia/papers/On_foundation_of_analytical_dynamics.pdf | archive-date = 2010-06-13 | citeseerx = 10.1.1.174.5726 }}</ref><ref name="Gay2018">{{Cite journal |last1=Gay-Balmaz |first1=François |last2=Yoshimura |first2=Hiroaki |year=2018 |title=From Lagrangian Mechanics to Nonequilibrium Thermodynamics: A Variational Perspective |journal=Entropy |language=en |volume=21 |issue=1 |pages=8 |doi=10.3390/e21010008 |pmid=33266724 |pmc=7514189 |arxiv=1904.03738 |bibcode=2018Entrp..21....8G |issn=1099-4300 |doi-access=free }}</ref>