d’Alembert’s principle

E158704

d’Alembert’s principle is a fundamental concept in classical mechanics that reformulates Newton’s laws to analyze the motion of systems by introducing inertial forces so they can be treated as if in static equilibrium.

All labels observed (3)

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Statements (46)

Predicate Object
instanceOf mechanical principle ⓘ
principle in classical mechanics ⓘ
appliesTo constrained mechanical systems ⓘ
rigid bodies ⓘ
systems of particles ⓘ
assumes Newtonian (non-relativistic) mechanics regime ⓘ
constraints are ideal (do no virtual work) ⓘ
category laws and principles in physics ⓘ
theoretical mechanics ⓘ
clarifies equivalence between Newtonian formulation and analytical mechanics ⓘ
treatment of non-inertial reference frames via inertial forces ⓘ
consequence eliminates explicit appearance of constraint forces in equations of motion ⓘ
leads to Lagrange’s equations of the first kind ⓘ
provides systematic method for handling holonomic constraints ⓘ
coreIdea introduces inertial forces to transform a dynamic problem into a static-equilibrium-like problem ⓘ
reduces dynamics to a problem of statics in an extended force system ⓘ
describes dynamics of mechanical systems ⓘ
reformulation of Newton’s laws of motion ⓘ
field analytical mechanics ⓘ
classical mechanics ⓘ
formalExpression ∑ᵢ (Fᵢ − mᵢ aᵢ) · δrᵢ = 0 ⓘ
hasAlternativeName dynamic equilibrium principle ⓘ
d’Alembert’s law of motion ⓘ
historicalPeriod 18th century ⓘ
involvesConcept constraint forces ⓘ
effective static equilibrium in an extended force system ⓘ
generalized forces ⓘ
inertial force ⓘ
virtual displacement ⓘ
mathematicalNature variational-like statement using virtual work ⓘ
namedAfter Jean le Rond d’Alembert ⓘ
linked to: Jean d’Alembert
relatedTo Hamilton’s principle ⓘ
Lagrangian mechanics ⓘ
Newton’s second law of motion ⓘ
generalized coordinates ⓘ
principle of virtual work ⓘ
states the sum of differences between applied forces and inertial forces for any virtual displacement consistent with constraints is zero ⓘ
usedFor analyzing constrained motion ⓘ
deriving equations of motion ⓘ
formulating Lagrange’s equations ⓘ
multibody dynamics ⓘ
usedIn engineering dynamics ⓘ
robotics modeling ⓘ
structural dynamics ⓘ
vehicle dynamics ⓘ
validWhen mass and acceleration are well-defined for each particle ⓘ

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Referenced by (7)

Full triples — surface form annotated when it differs from this entity's canonical label.

Jean d’Alembert → notableWork → d’Alembert’s principle ⓘ
Jean d’Alembert → knownFor → d’Alembert’s principle ⓘ
d’Alembert’s principle → hasAlternativeName → d’Alembert’s law of motion ⓘ
linked to: d’Alembert’s principle
d’Alembert’s principle → hasAlternativeName → dynamic equilibrium principle ⓘ
linked to: d’Alembert’s principle
Traité de dynamique → mainSubject → d’Alembert’s principle ⓘ
Traité de dynamique → introducedConcept → d’Alembert’s principle ⓘ
Traité de dynamique → associatedPrinciple → d’Alembert’s principle ⓘ