CM:001A force law is incomplete until its frame and dimensions are declaredView problem statementNewtonian Mechanics And Conservation LawsForce Law AuditGalilean CovarianceDimensional ConsistencyNewtonian mechanics and conservation lawsClassical Mechanics · Theorem—
CM:002Central internal forces vanish from the total torque balanceView access optionsNewtonian Mechanics And Conservation LawsAngular Momentum BalanceCentral Pair ForceExternal TorqueNewtonian mechanics and conservation lawsClassical Mechanics · Theorem—
CM:003Angular momentum about a translating point carries a transport termView access optionsNewtonian Mechanics And Conservation LawsMoving OriginTransport TorqueMomentum CouplingNewtonian mechanics and conservation lawsClassical Mechanics · Proof—
CM:004A finite-time virial identity keeps the endpoint term textbooks dropView access optionsNewtonian Mechanics And Conservation LawsFinite Time VirialEndpoint CorrectionHomogeneous PotentialNewtonian mechanics and conservation lawsClassical Mechanics · Proof—
CM:005A uniformly accelerating frame shifts a harmonic equilibriumView access optionsNewtonian Mechanics And Conservation LawsTranslating FrameFictitious PotentialShifted EquilibriumNewtonian mechanics and conservation lawsClassical Mechanics · Calculation—
CM:006When time-translation symmetry really does—and does not—conserve mechanical energyView access optionsNewtonian Mechanics And Conservation LawsLagrangian Energy BalanceTime Translation SymmetryParametric Power AuditNewtonian mechanics and conservation lawsClassical Mechanics · Mixed review—
CM:007A Galilean boost changes kinetic energy but not collision feasibilityView access optionsNewtonian Mechanics And Conservation LawsGalilean BoostEnergy Frame ShiftCollision InvariantsNewtonian mechanics and conservation lawsClassical Mechanics · Mixed review—
CM:008Spin angular momentum separates cleanly from barycenter motionView access optionsNewtonian Mechanics And Conservation LawsSpin Orbital SplitBarycentric CoordinatesOrigin IndependenceNewtonian mechanics and conservation lawsClassical Mechanics · Proof—
CM:009An accelerating incident stream tests the full Meshchersky balanceView access optionsNewtonian Mechanics And Conservation LawsMeshhersky EquationAccelerating StreamOpen System MomentumNewtonian mechanics and conservation lawsClassical Mechanics · Calculation—
CM:010A double-well phase portrait separates trapped, separatrix, and crossing motionView access optionsNewtonian Mechanics And Conservation LawsDouble Well Phase PortraitSeparatrix ClassificationNonlinear StabilityNewtonian mechanics and conservation lawsClassical Mechanics · Calculation—
CM:011Pendulum time diverges logarithmically on approach to the separatrixView access optionsNewtonian Mechanics And Conservation LawsSeparatrix Time DivergencePendulum QuadratureElliptic Integral AsymptoticsNewtonian mechanics and conservation lawsClassical Mechanics · Calculation—
CM:012A common body force leaves every relative momentum unchangedView access optionsNewtonian Mechanics And Conservation LawsEquivalence PrincipleRelative MomentumUniform Body ForceNewtonian mechanics and conservation lawsClassical Mechanics · Theorem—
CM:013Internal viscous coupling damps relative motion while preserving total momentumView access optionsNewtonian Mechanics And Conservation LawsInternal DampingRelative ModeMomentum ConservationNewtonian mechanics and conservation lawsClassical Mechanics · Calculation—
CM:014Jacobi coordinates diagonalize three-particle kinetic energyView access optionsNewtonian Mechanics And Conservation LawsJacobi CoordinatesKinetic Energy SplitThree Body ReductionNewtonian mechanics and conservation lawsClassical Mechanics · Proof—
CM:015An ideal impulsive rod constraint projects relative velocityView access optionsNewtonian Mechanics And Conservation LawsConstraint ImpulseMass Metric ProjectionInelastic CaptureNewtonian mechanics and conservation lawsClassical Mechanics · Calculation—
CM:016Uniform forcing conserves a many-particle pseudomomentumView access optionsNewtonian Mechanics And Conservation LawsPseudomomentumUniform ForcingAccelerated Frame InvariantNewtonian mechanics and conservation lawsClassical Mechanics · Theorem—
CM:017Translation and rotation symmetries follow directly from pair potentialsView access optionsNewtonian Mechanics And Conservation LawsPair PotentialTranslation SymmetryRotation SymmetryNewtonian mechanics and conservation lawsClassical Mechanics · Theorem—
CM:018Time reversal requires the force law to transform with velocityView access optionsNewtonian Mechanics And Conservation LawsTime ReversalVelocity Dependent ForceTrajectory SymmetryNewtonian mechanics and conservation lawsClassical Mechanics · Concept & counterexample—
CM:019A skew velocity coupling preserves mechanical energyView access optionsNewtonian Mechanics And Conservation LawsSkew CouplingEnergy PreservationVelocity Dependent ForceNewtonian mechanics and conservation lawsClassical Mechanics · Theorem—
CM:020A discrete spatial symmetry does not create angular-momentum conservationView access optionsNewtonian Mechanics And Conservation LawsDiscrete SymmetryContinuous RotationTorque CounterexampleNewtonian mechanics and conservation lawsClassical Mechanics · Concept & counterexample—
CM:021The Lagrange-Jacobi identity diagnoses expansion in an N-body snapshotView access optionsNewtonian Mechanics And Conservation LawsLagrange Jacobi IdentityN Body InertiaHomogeneous PotentialNewtonian mechanics and conservation lawsClassical Mechanics · Theorem—
CM:022A time-dependent rotation matrix yields every inertial acceleration termView access optionsNewtonian Mechanics And Conservation LawsRotation Matrix TheoremTime Dependent FramesCoriolis Euler CentrifugalNewtonian mechanics and conservation lawsClassical Mechanics · Theorem—
CM:023Uniform rotation conserves a Jacobi integral, not ordinary rotating-frame energyView access optionsNewtonian Mechanics And Conservation LawsJacobi IntegralUniformly Rotating FrameEffective PotentialNewtonian mechanics and conservation lawsClassical Mechanics · Calculation—
CM:024Foucault precession retains only Earth's vertical rotation componentView access optionsNewtonian Mechanics And Conservation LawsFoucault PendulumCoriolis PrecessionLatitude DependenceNewtonian mechanics and conservation lawsClassical Mechanics · Theorem—