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Canonical static concept record

Equation of motion

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Summary

An equation determining allowed histories or evolution from the dynamical variables and initial or boundary data.

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Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Physical lawEquation of motion

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Equations of motion are dynamical physical laws for histories or states.

How to interpret this relation type

A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.

Relation sources

Potential-energy surfaceEquation of motion

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Within an adiabatic electronic-state approximation, gradients of a molecular potential-energy surface supply forces in nuclear equations of motion; nonadiabatic transitions require coupled surfaces and additional terms.

How to interpret this relation type

A theory, law, or interaction describes the behavior of the target within a stated regime. The edge detail must state important limits or qualifications.

Relation sources

Stationary-action principleEquation of motion

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Variation of the action yields equations of motion under appropriate boundary conditions.

How to interpret this relation type

Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.

Relation sources

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Equation of motionEuler–Lagrange equation

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Euler–Lagrange equations are the equations of motion obtained by stationarity of a Lagrangian action.

How to interpret this relation type

The target is a member or subtype of the broader source class.

Relation sources