d’Alembert’s principle

E158704

mechanical principle principle in classical mechanics

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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All labels observed (3)

Label	Occurrences
d’Alembert’s principle canonical	5
dynamic equilibrium principle	1
d’Alembert’s law of motion	1

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 ⓘ 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 ⓘ

How these facts were elicited

The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.

Instruction

You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10.

# Requirements
- If you don't know the subject at all, return an empty list.
- If the subject is not a named entity, return an empty list.
- Include at least one triple where predicate is "instanceOf".
- Do not get too wordy.
- Separate several objects into multiple triples with one object.

Input

Subject: d’Alembert’s principle
Description of subject: 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.

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 ⓘ