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CM:001A force law is incomplete until its frame and dimensions are declared

Newtonian Mechanics And Conservation LawsForce Law AuditGalilean CovarianceDimensional Consistency

Newtonian mechanics and conservation lawsClassical Mechanics · Theorem

CM:002Central internal forces vanish from the total torque balance

Newtonian Mechanics And Conservation LawsAngular Momentum BalanceCentral Pair ForceExternal Torque

Newtonian mechanics and conservation lawsClassical Mechanics · Theorem

CM:003Angular momentum about a translating point carries a transport term

Newtonian Mechanics And Conservation LawsMoving OriginTransport TorqueMomentum Coupling

Newtonian mechanics and conservation lawsClassical Mechanics · Proof

CM:004A finite-time virial identity keeps the endpoint term textbooks drop

Newtonian Mechanics And Conservation LawsFinite Time VirialEndpoint CorrectionHomogeneous Potential

Newtonian mechanics and conservation lawsClassical Mechanics · Proof

CM:005A uniformly accelerating frame shifts a harmonic equilibrium

Newtonian Mechanics And Conservation LawsTranslating FrameFictitious PotentialShifted Equilibrium

Newtonian mechanics and conservation lawsClassical Mechanics · Calculation

CM:006When time-translation symmetry really does—and does not—conserve mechanical energy

Newtonian Mechanics And Conservation LawsLagrangian Energy BalanceTime Translation SymmetryParametric Power Audit

Newtonian mechanics and conservation lawsClassical Mechanics · Mixed review

CM:007A Galilean boost changes kinetic energy but not collision feasibility

Newtonian Mechanics And Conservation LawsGalilean BoostEnergy Frame ShiftCollision Invariants

Newtonian mechanics and conservation lawsClassical Mechanics · Mixed review

CM:008Spin angular momentum separates cleanly from barycenter motion

Newtonian Mechanics And Conservation LawsSpin Orbital SplitBarycentric CoordinatesOrigin Independence

Newtonian mechanics and conservation lawsClassical Mechanics · Proof

CM:009An accelerating incident stream tests the full Meshchersky balance

Newtonian Mechanics And Conservation LawsMeshhersky EquationAccelerating StreamOpen System Momentum

Newtonian mechanics and conservation lawsClassical Mechanics · Calculation

CM:010A double-well phase portrait separates trapped, separatrix, and crossing motion

Newtonian Mechanics And Conservation LawsDouble Well Phase PortraitSeparatrix ClassificationNonlinear Stability

Newtonian mechanics and conservation lawsClassical Mechanics · Calculation

CM:011Pendulum time diverges logarithmically on approach to the separatrix

Newtonian Mechanics And Conservation LawsSeparatrix Time DivergencePendulum QuadratureElliptic Integral Asymptotics

Newtonian mechanics and conservation lawsClassical Mechanics · Calculation

CM:012A common body force leaves every relative momentum unchanged

Newtonian Mechanics And Conservation LawsEquivalence PrincipleRelative MomentumUniform Body Force

Newtonian mechanics and conservation lawsClassical Mechanics · Theorem

CM:013Internal viscous coupling damps relative motion while preserving total momentum

Newtonian Mechanics And Conservation LawsInternal DampingRelative ModeMomentum Conservation

Newtonian mechanics and conservation lawsClassical Mechanics · Calculation

CM:014Jacobi coordinates diagonalize three-particle kinetic energy

Newtonian Mechanics And Conservation LawsJacobi CoordinatesKinetic Energy SplitThree Body Reduction

Newtonian mechanics and conservation lawsClassical Mechanics · Proof

CM:015An ideal impulsive rod constraint projects relative velocity

Newtonian Mechanics And Conservation LawsConstraint ImpulseMass Metric ProjectionInelastic Capture

Newtonian mechanics and conservation lawsClassical Mechanics · Calculation

CM:016Uniform forcing conserves a many-particle pseudomomentum

Newtonian Mechanics And Conservation LawsPseudomomentumUniform ForcingAccelerated Frame Invariant

Newtonian mechanics and conservation lawsClassical Mechanics · Theorem

CM:017Translation and rotation symmetries follow directly from pair potentials

Newtonian Mechanics And Conservation LawsPair PotentialTranslation SymmetryRotation Symmetry

Newtonian mechanics and conservation lawsClassical Mechanics · Theorem

CM:018Time reversal requires the force law to transform with velocity

Newtonian Mechanics And Conservation LawsTime ReversalVelocity Dependent ForceTrajectory Symmetry

Newtonian mechanics and conservation lawsClassical Mechanics · Concept & counterexample

CM:019A skew velocity coupling preserves mechanical energy

Newtonian Mechanics And Conservation LawsSkew CouplingEnergy PreservationVelocity Dependent Force

Newtonian mechanics and conservation lawsClassical Mechanics · Theorem

CM:020A discrete spatial symmetry does not create angular-momentum conservation

Newtonian Mechanics And Conservation LawsDiscrete SymmetryContinuous RotationTorque Counterexample

Newtonian mechanics and conservation lawsClassical Mechanics · Concept & counterexample

CM:021The Lagrange-Jacobi identity diagnoses expansion in an N-body snapshot

Newtonian Mechanics And Conservation LawsLagrange Jacobi IdentityN Body InertiaHomogeneous Potential

Newtonian mechanics and conservation lawsClassical Mechanics · Theorem

CM:022A time-dependent rotation matrix yields every inertial acceleration term

Newtonian Mechanics And Conservation LawsRotation Matrix TheoremTime Dependent FramesCoriolis Euler Centrifugal

Newtonian mechanics and conservation lawsClassical Mechanics · Theorem

CM:023Uniform rotation conserves a Jacobi integral, not ordinary rotating-frame energy

Newtonian Mechanics And Conservation LawsJacobi IntegralUniformly Rotating FrameEffective Potential

Newtonian mechanics and conservation lawsClassical Mechanics · Calculation

CM:024Foucault precession retains only Earth's vertical rotation component

Newtonian Mechanics And Conservation LawsFoucault PendulumCoriolis PrecessionLatitude Dependence

Newtonian mechanics and conservation lawsClassical Mechanics · Theorem

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CM:001A force law is incomplete until its frame and dimensions are declaredView problem statement

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CM:001A force law is incomplete until its frame and dimensions are declaredView problem statement

CM:001A force law is incomplete until its frame and dimensions are declared

CM:001A force law is incomplete until its frame and dimensions are declared