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.

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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
Lagrangian mechanics
surface form: 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 d’Alembert’s principle
surface form: dynamic equilibrium principle

d’Alembert’s principle
surface form: 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 d’Alembert
surface form: Jean le Rond d’Alembert
relatedTo principle of least action
surface form: Hamilton’s principle

Lagrangian mechanics
Newton's second law of motion
surface form: 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 principle
this entity surface form: d’Alembert’s law of motion
d’Alembert’s principle hasAlternativeName d’Alembert’s principle
this entity surface form: dynamic equilibrium 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