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)
| Label | Occurrences |
|---|---|
| d’Alembert’s principle canonical | 5 |
| dynamic equilibrium principle | 1 |
| d’Alembert’s law of motion | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1380673 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
Target entity: d’Alembert’s principle Context triple: [Jean d’Alembert, notableWork, d’Alembert’s principle]
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A.
principle of least action
The principle of least action is a fundamental concept in physics stating that the path taken by a physical system between two states is the one for which a specific quantity called the action is minimized (or made stationary), forming the basis of Lagrangian and Hamiltonian mechanics.
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B.
Euler–Lagrange equation
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
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C.
Lagrangian mechanics
Lagrangian mechanics is a reformulation of classical mechanics that uses energy-based principles and the calculus of variations to derive the equations of motion for physical systems.
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D.
Mécanique analytique
Mécanique analytique is Lagrange’s landmark 1788 treatise that reformulated classical mechanics using variational principles and generalized coordinates, laying the foundations of analytical mechanics.
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E.
Noether's theorem
Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: d’Alembert’s principle Target entity description: 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.
-
A.
principle of least action
The principle of least action is a fundamental concept in physics stating that the path taken by a physical system between two states is the one for which a specific quantity called the action is minimized (or made stationary), forming the basis of Lagrangian and Hamiltonian mechanics.
-
B.
Euler–Lagrange equation
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
-
C.
Lagrangian mechanics
Lagrangian mechanics is a reformulation of classical mechanics that uses energy-based principles and the calculus of variations to derive the equations of motion for physical systems.
-
D.
Mécanique analytique
Mécanique analytique is Lagrange’s landmark 1788 treatise that reformulated classical mechanics using variational principles and generalized coordinates, laying the foundations of analytical mechanics.
-
E.
Noether's theorem
Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.
- F. None of above. chosen
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
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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.