Classical Mechanics¶
Goldstein, H., Poole, C. P., & Safko, J. L. (2002). Classical Mechanics. Addison-Wesley.
Cited by¶
12 citations across 12 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Axiom
- Scientific modelling — conservation laws and the postulates of a physical theory, each tradition stipulating a small set of axioms and deriving the rest.
This sourceStandard graduate mechanics text presenting a physical theory from stipulated postulates (Newton's laws / variational principles), from which the conservation laws of energy, linear, and angular momentum are derived.
Supported in partVerified against the work's full text
Goldstein builds mechanics from one basic postulate (Hamilton's principle or Newton's laws) and derives the conservation theorems, which he treats as derived results, not axioms.
“construct the mechanics of monogenic systems from Hamil¬ ton’s principle as the basic postulate rather than Newton’s laws of motion”
- Scientific modelling — conservation laws and the postulates of a physical theory, each tradition stipulating a small set of axioms and deriving the rest.
- Conjugate Variables
This sourceStandard treatment of canonical transformations, Poisson brackets, and Hamilton-Jacobi theory underlying conjugate variables.
- Damping
- Physics Damped harmonic oscillator
This sourceGraduate text treating damped oscillators in Lagrangian/Hamiltonian form, dissipative forces ('Forced Vibrations and the Effect of Dissipative Forces'), and dissipation–time-reversal links.
SupportedVerified against the work's full text
Goldstein's graduate mechanics text lists the driven-damped harmonic oscillator and dissipative forces among the oscillation topics it treats.
“Driven-damped Harmonic Oscillator, and Parametric”
- Physics Damped harmonic oscillator
- Degrees of Freedom
- Textbook treatments by Goldstein, Poole & Safko (2002)
SupportedVerified against the work's full text
Goldstein, Poole and Safko give the textbook DOF count: 3N for free particles, 3N - k under k holonomic constraints; the preface calls the book the standard graduate text.
“A system of N particles, free from constraints, has 3 N independent coordinates or degrees of freedom.”
- Textbook treatments by Goldstein, Poole & Safko (2002)
- Minimal Modification Principle
- Minimal Modification Principle is about how we construct alternative scenarios for reasoning; it is not a claim about physical reality or how systems evolve, as Goldstein, Poole, and Safko (2002) develop the variational principles that govern actual physical evolution rather than counterfactual reasoning.
This sourceComprehensive pedagogical treatment of damped oscillators in the Lagrangian and Hamiltonian frameworks; covers dissipative forces, energy dissipation, and the connection between dissipation and time-reversal symmetry breaking; standard reference for graduate-level classical mechanics.
Supported in partVerified against the work's full text
Goldstein et al. supports that variational principles such as Hamilton's principle govern the actual motion of mechanical systems; it says nothing about counterfactual reasoning or the Minimal Modification Principle.
“out of all possible paths by which the system point could travel from its position at time ti to its position at time t2, it will actually travel along that path for which the value of the integral (2.1) is stationary.”
- Minimal Modification Principle is about how we construct alternative scenarios for reasoning; it is not a claim about physical reality or how systems evolve, as Goldstein, Poole, and Safko (2002) develop the variational principles that govern actual physical evolution rather than counterfactual reasoning.
- Noether's Theorem
- The pedagogical exposition in Goldstein-Poole-Safko (2002)
This sourceComprehensive pedagogical treatment of damped oscillators in the Lagrangian and Hamiltonian frameworks; covers dissipative forces, energy dissipation, and the connection between dissipation and time-reversal symmetry breaking; standard reference for graduate-level classical mechanics.
- The pedagogical exposition in Goldstein-Poole-Safko (2002)
- Principle of Least Action
- Modern textbooks ,
This sourceComprehensive pedagogical treatment of damped oscillators in the Lagrangian and Hamiltonian frameworks; covers dissipative forces, energy dissipation, and the connection between dissipation and time-reversal symmetry breaking; standard reference for graduate-level classical mechanics.
- Modern textbooks ,
Domain-specific¶
- Classical mechanics
- Derivative
- In classical mechanics, velocity is the derivative of position with respect to time and acceleration is the derivative of velocity, so Newton's second law F = ma = m d²x/dt² is a second-order differential equation
This sourceGoldstein's statement that the mechanics of a particle is contained in Newton's second law of motion and that the equation of motion reduces to a single second-order differential equation.
Supported in partVerified against a saved copy of the source
“mechanics of the particle is contained in Newton\u2019s second law of motion”
- In classical mechanics, velocity is the derivative of position with respect to time and acceleration is the derivative of velocity, so Newton's second law F = ma = m d²x/dt² is a second-order differential equation
- Momentum
- Momentum's structural commitments are precise and load-bearing: it is additive over the parts of a system (the total momentum of a composite system is the vector sum of the momenta of its parts), it is exchanged in collisions and interactions in a bookkeeping that balances exactly (impulse, the time-integral of force, is the amount by which one system's momentum changes at the expense of another's), and it stands in a canonical conjugate relation with position that is not algebraic convenience but a fundamental geometric fact — in Hamiltonian mechanics the pair \((x, p)\) is the conjugate pair on which the symplectic structure is built, and in quantum mechanics \(\hat{p} = -i\hbar \partial/\partial x\) is the generator of spatial translations with the canonical commutation relation \([\hat{x}, \hat{p}] = i\hbar\) encoding Heisenberg's uncertainty principle
This sourceGoldstein's treatment of conjugate momentum and canonical transformations, in which a coordinate's conjugate momentum corresponds to a translation of the system and the classical Poisson bracket is replaced by the commutator of quantum operators.
Supported in partVerified against the work's full text
“The Symplectic Approach to Canonical Transformations 381”
- Momentum's structural commitments are precise and load-bearing: it is additive over the parts of a system (the total momentum of a composite system is the vector sum of the momenta of its parts), it is exchanged in collisions and interactions in a bookkeeping that balances exactly (impulse, the time-integral of force, is the amount by which one system's momentum changes at the expense of another's), and it stands in a canonical conjugate relation with position that is not algebraic convenience but a fundamental geometric fact — in Hamiltonian mechanics the pair \((x, p)\) is the conjugate pair on which the symplectic structure is built, and in quantum mechanics \(\hat{p} = -i\hbar \partial/\partial x\) is the generator of spatial translations with the canonical commutation relation \([\hat{x}, \hat{p}] = i\hbar\) encoding Heisenberg's uncertainty principle
- Rigid rotor
Mechanisms¶
- Poisson-Bracket Identity Test
- What distinguishes it is that the whole test is symbolic algebra on the coordinate functions — it needs no trajectories, no plots, and no list of physical invariants; the fundamental brackets alone settle canonicity.
This sourceShows that symbolic preservation of the fundamental Poisson brackets is sufficient to establish that a coordinate transformation is canonical.
- What distinguishes it is that the whole test is symbolic algebra on the coordinate functions — it needs no trajectories, no plots, and no list of physical invariants; the fundamental brackets alone settle canonicity.
Verification¶
Does it exist? Confirmed. This work's ISBN resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 6 of 12 citations: 2 supported, 4 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
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Links previously used in the corpus¶
Before the registry existed this work was also linked 3 other ways.
- https://openlibrary.org/isbn/9780201657029 ×2
- https://archive.org/details/HerbertGoldsteinCharlesPooleJohnSafkoClassicalMechanics3rdEd ×1
- https://www.pearson.com/en-us/subject-catalog/p/classical-mechanics/P200000006871/9780201657029 ×1
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