Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-17T06:31:01.729Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  28 July 2018

Nivaldo A. Lemos
Affiliation:
Universidade Federal Fluminense, Brazil
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Analytical Mechanics , pp. 442 - 451
Publisher: Cambridge University Press
Print publication year: 2018

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abraham, R. & Marsden, J. E. (1978). Foundations of Mechanics, 2nd edn. London: Benjamin/Cummmings.Google Scholar
Almeida, M. A., Moreira, I. C. & Santos, F. C. (1998). On the Ziglin-Yoshida analysis for some classes of homogeneous Hamiltonian systems. Brazilian Journal of Physics, 28, 470480.Google Scholar
Almeida, M. A., Moreira, I. C. & Yoshida, H. (1992). On the non-integrability of the Störmer problem. Journal of Physics A: Mathematical and General, 25, L227–L230.CrossRefGoogle Scholar
Anderson, J. L. (1990). Newton’s first two laws of motion are not definitions. American Journal of Physics, 58, 11921195.CrossRefGoogle Scholar
Andersson, K. G. (1994). Poincaré’s discovery of homoclinic points. Archive for History of Exact Sciences, 48, 133147.CrossRefGoogle Scholar
Aravind, P. K. (1989). Geometrical interpretation of the simultaneous diagonalization of two quadratic forms. American Journal of Physics, 57, 309311.CrossRefGoogle Scholar
Arfken, G. B. & Weber, H. J. (1995). Mathematical Methods for Physicists, 4th edn. New York: Academic Press.Google Scholar
Armitage, J. V. & Eberlein, W. F. (2006). Elliptic Functions. Cambridge: Cambridge University Press.Google Scholar
Arnold, V. I. (1963). Proof of a theorem of A. N. Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian. Russian Mathematical Surveys, 18(5), 936.Google Scholar
Arnold, V. I. (1989). Mathematical Methods of Classical Mechanics, 2nd edn. New York: Springer.CrossRefGoogle Scholar
Arnold, V. I., Kozlov, V. V. & Neishtadt, A. I. (2006). Mathematical Aspects of Classical and Celestial Mechanics, 3rd edn. Berlin: Springer.Google Scholar
Arnowitt, R., Deser, S. & Misner, C. W. (1962). The Dynamics of General Relativity. In Witten, L., ed., Gravitation: An Introduction to Current Research. New York: Wiley, pp. 227264. arXiv:gr-qc/0405109v1.Google Scholar
Barrow-Green, J. (1994). Oscar II’s prize competition and the error in Poincaré’s memoir on the three body problem. Archive for History of Exact Sciences, 48, 107131.Google Scholar
Barrow-Green, J. (1997). Poincaré and the Three Body Problem. Providence, RI: American Mathematical Society.Google Scholar
Barrow-Green, J. (2010). The dramatic episode of Sundman. Historia Mathematica, 37, 164203. www.sciencedirect.com/science/article/pii/S0315086009001360.Google Scholar
Bartucelli, M. & Gentile, G. (2002). Lindstedt series for perturbations of isochronous systems: A review of the general theory. Reviews in Mathematical Physics, 14, 121171.Google Scholar
Barut, A. O. (1980). Electrodynamics and Classical Theory of Fields and Particles. New York: Dover.Google Scholar
Bateman, H. (1931). On dissipative systems and related variational principles. Physical Review, 38, 815819.CrossRefGoogle Scholar
Benettin, G., Galgani, L., Giorgilli, A. & Strelcyn, J.-M. (1984). A proof of Kolmogorov’s theorem on invariant tori using canonical transformations defined by the Lie method. Nuovo Cimento B, 79, 201223.CrossRefGoogle Scholar
Bergmann, P. G. (1976). Introduction to the Theory of Relativity. New York: Dover.Google Scholar
Berry, M. V. (1978). Regular and Irregular Motion. In Jorna, S., ed., Topics in Nonlinear Dynamics: A Tribute to Sir Edward Bullard. New York: American Institute of Physics, pp. 16120.Google Scholar
Berry, M. V. (1985). Classical adiabatic angles and quantal adiabatic phase. Journal of Physics A: Mathematical and General, 18, 1527.CrossRefGoogle Scholar
Bertrand, J. (1873). Théorème relatif au mouvement d’un point attire vers un centre fixe. Comptes Rendus de l’Académie des Sciences de Paris, 77, 849853. English translation by Santos, F. C., Soares, V. and Tort, A. C. (2011). An English translation of Bertrand’s theorem. Latin American Journal of Physics Education, 5, 694–696. arXiv:0704.2396.Google Scholar
Boas, R. P. Jr. (1996). A Primer of Real Functions, 4th edn. Washington, DC: The Mathematical Association of America.Google Scholar
Bordemann, M. (2008). Deformation quantization: A survey. Journal of Physics: Conference Series, 103, 131.Google Scholar
Bottazzini, U. & Gray, J. (2013). Hidden Harmony-Geometric Fantasies: The Rise of Complex Function Theory. New York: Springer.Google Scholar
Braun, M. (1981). Mathematical remarks on the Van Allen radiation belt: A survey of old and new results. SIAM Review, 23, 6193.CrossRefGoogle Scholar
Bricmont, J. (1996). Science of chaos or chaos in science? arXiv:chao-dyn/9603009.Google Scholar
Cadoni, M., Carta, P. & Mignemi, S. (2000). Realization of the infinite-dimensional symmetries of conformal mechanics. Physical Review D, 62, 086002–1–4.CrossRefGoogle Scholar
Callen, H. (1960). Thermodynamics. New York: Wiley.Google Scholar
Cary, J. R. (1981). Lie transform perturbation theory for Hamiltonian systems. Physics Reports, 79, 129159.CrossRefGoogle Scholar
Casasayas, J., Nunes, A. & Tufillaro, N. (1990). Swinging Atwood’s machine: Integrability and dynamics. Journal de Physique, 51, 16931702.CrossRefGoogle Scholar
Casey, J. (2014). Applying the principle of angular momentum to constrained systems of point masses. American Journal of Physics, 82, 165168. Casey, J. (2015). Erratum. American Journal of Physics, 83, 185.Google Scholar
Cercignani, C. (1998). Ludwig Boltzmann: The Man Who Trusted Atoms. Oxford: Oxford University Press.Google Scholar
Chagas, E. F. das & Lemos, N. A. (1981). Um exemplo de como não usar teoremas matemáticos em problemas físicos. Revista Brasileira de Física, 11, 481488.Google Scholar
Chandre, C. & Jauslin, H. R. (1998). A version of Thirring’s approach to the Kolmogorov-Arnold-Moser theorem for quadratic Hamiltonians with degenerate twist. Journal of Mathematical Physics, 39, 58565865.Google Scholar
Christ, N. H. & Lee, T. D. (1980). Operator ordering and Feynman rules in gauge theories. Physical Review D, 22, 939958.CrossRefGoogle Scholar
Corben, H. C. & Stehle, P. (1960). Classical Mechanics. New York: Dover.Google Scholar
Courant, R. & Hilbert, D. (1953). Methods of Mathematical Physics. Vol. I. New York: Interscience Publishers.Google Scholar
Crawford, F. S. (1990). Elementary examples of adiabatic invariance. American Journal of Physics, 58, 337344.Google Scholar
Davydov, A. S. (1973). The theory of contraction of proteins under their excitation. Journal of Theoretical Biology, 38, 559569.Google Scholar
Deser, S., Jackiw, R. & Templeton, S. (1982). Topologically massive gauge theories. Annals of Physics, 140, 372411.CrossRefGoogle Scholar
Desloge, E. A. (1982). Classical Mechanics, 2 vols. Malabar, FL: Robert E. Krieger.Google Scholar
Dettman, J. W. (1986). Introduction to Linear Algebra and Differential Equations. New York: Dover.Google Scholar
Dhar, A. (1993). Nonuniqueness in the solutions of Newton’s equations of motion. American Journal of Physics, 61, 5861.Google Scholar
Diacu, F. (1996). The Solution of the n-body Problem. The Mathematical Intelligencer, 18(3), 6670.Google Scholar
Diacu, F. & Holmes, P. (1996). Celestial Encounters: The Origins of Chaos and Stability. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Dilão, R. & Alves-Pires, R. (2007). Chaos in the Störmer problem. arXiv:0704.3250v1.Google Scholar
Dirac, P. A. M. (1964). Lectures on Quantum Mechanics. New York: Yeshiva University.Google Scholar
Dugas, R. (1988). A History of Mechanics. New York: Dover.Google Scholar
Dumas, H. S. (2014). The KAM Story. New Jersey: World Scientific.CrossRefGoogle Scholar
Eisenbud, L. (1958). On the classical laws of motion. American Journal of Physics, 26, 144159.Google Scholar
Eliasson, L. H. (1996). Absolutely convergent series expansions for quasi periodic motions. Mathematical Physics Electronic Journal, 2(4), 133.Google Scholar
Elsgoltz, L. (1969). Ecuaciones Diferenciales y Cálculo Variacional. Moscow: Mir Publishers.Google Scholar
Epstein, S. T. (1982). The angular velocity of a rotating rigid body. American Journal of Physics, 50, 948.CrossRefGoogle Scholar
Farina de Souza, C. and Gandelman, M. M. (1990). An algebraic approach for solving mechanical problems. American Journal of Physics, 58, 491495.Google Scholar
Fasano, A. & Marmi, S. (2006). Analytical Mechanics. Oxford: Oxford University Press.CrossRefGoogle Scholar
Fetter, A. L. & Walecka, J. D. (1980). Theoretical Mechanics of Particles and Continua. New York: McGraw-Hill.Google Scholar
Feynman, R. P. (1985). Surely You’re Joking, Mr. Feynman! New York: Bantam Books.Google Scholar
Feynman, R. P. & Hibbs, A. (1965). Quantum Mechanics and Path Integrals. New York: McGraw-Hill.Google Scholar
Feynman, R. P., Leighton, R. B. & Sands, M. (1963). The Feynman Lectures on Physics, 3 vols. Reading, MA: Addison-Wesley.Google Scholar
Flanders, H. (1989). Differential Forms with Applications to the Physical Sciences. New York: Dover.Google Scholar
Fox, C. (1987). An Introduction to the Calculus of Variations. New York: Dover.Google Scholar
Gallavotti, G. (1983). The Elements of Mechanics. New York: Springer.CrossRefGoogle Scholar
Gallavotti, G. (1999). Statistical Mechanics: A Short Treatise. Berlin: Springer.Google Scholar
Gangopadhyaya, A. & Ramsey, G. (2013). Unintended consequences of imprecise notation: An example from mechanics. American Journal of Physics, 81, 313315.Google Scholar
Gantmacher, F. (1970). Lectures in Analytical Mechanics. Moscow: Mir Publishers.Google Scholar
Gelfand, I. M. & Fomin, S. V. (1963). Calculus of Variations. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Giorgilli, A., Locatelli, U. & Sansottera, M. (2013). Kolmogorov and Nekhoroshev theory for the problem of three bodies. arXiv:1303.7395v1.Google Scholar
Gleiser, R. J. & Kozameh, C. N. (1980). A simple application of adiabatic invariance. American Journal of Physics, 48, 756759.Google Scholar
Goldstein, H. (1980). Classical Mechanics, 2nd edn. Reading, MA: Addison-Wesley.Google Scholar
Goriely, A. (2001). Integrability and Nonintegrability of Dynamical Systems. New Jersey: World Scientific.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. (1980). Tables of Integrals, Series and Products. New York: Academic Press.Google Scholar
Gray, C. G. & Taylor, E. F. (2007). When action is not least. American Journal of Physics, 75, 434458.Google Scholar
Gutiérrez-López, S., Castellanos-Moreno, A. & Rosas-Burgos, R. A. (2008). A new constant of motion for an electric charge acted on by a point electric dipole. American Journal of Physics, 76, 11411145.Google Scholar
Halmos, P. R. (1974). Finite-Dimensional Vector Spaces. New York: Springer.Google Scholar
Hamermesh, M. (1962). Group Theory and Its Application to Physical Problems. New York: Dover.CrossRefGoogle Scholar
Hamilton, W. R. (1834). On a General Method in Dynamics. In Philosophical Transactions of the Royal Society, Part II, 247–308.Google Scholar
Hamilton, W. R. (1835). Second Essay on a General Method in Dynamics. In Philosophical Transactions of the Royal Society, Part I, 95–144.Google Scholar
Hand, L. N. & Finch, J. D. (1998). Analytical Mechanics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hartmann, H. (1972). Die Bewegung eines Körpers in einem ringförmigen Potentialfeld. Theoretica Chimica Acta, 24, 201206.Google Scholar
Havas, P. (1957). The range of application of the Lagrange formalism - I. Nuovo Cimento Supplement, 5, 363388.Google Scholar
Hawking, S. W. & Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time. Cambridge: Cambridge University Press.Google Scholar
Henneaux, M. & Shepley, L. C. (1982). Lagrangians for spherically symmetric potentials. Journal of Mathematical Physics, 23, 21012107.Google Scholar
Henneaux, M. & Teitelboim, C. (1992). Quantization of Gauge Systems. New Jersey: Princeton University Press.Google Scholar
Hietarinta, J. (1984). New integrable Hamiltonians with transcendental invariants. Physical Review Letters, 52, 10571060.Google Scholar
Hoffman, K. & Kunze, R. (1971). Linear Algebra, 2nd edn. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Huang, K. (1963). Statistical Mechanics. New York: Wiley.Google Scholar
Ichtiaroglou, S. (1997). Non-integrability in Hamiltonian mechanics. Celestial Mechanics and Dynamical Astronomy, 65, 2131.Google Scholar
Ivancevic, S. & Pearce, C. E. M. (2001). Poisson manifolds in generalised Hamiltonian biomechanics. Bulletin of the Australian Mathematical Society, 64, 515526.Google Scholar
Jackson, J. D. (1999). Classical Electrodynamics, 3rd edn. New York: Wiley.Google Scholar
Jacobi, C. G. J. (1837). Über die reduction der partiellen Differentialgleichungen erster Ordnung zwischen irgend einer Zahl Variabeln auf die Integration eines einzigen Systems gewöhnlicher Differentialgleichungen. Crelle Journal fur die Reine und Angewandte Mathematik, 17, 97162. Vol. IV of Oeuvres Complètes. http://sites.mathdoc.fr/OEUVRES/.Google Scholar
Jones, R. S. (1995). Circular motion of a charged particle in an electric dipole field. American Journal of Physics, 63, 10421043.CrossRefGoogle Scholar
José, J. V. & Saletan, E. J. (1998). Classical Dynamics: A Contemporary Approach. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Karatas, D. L. & Kowalski, K. L. (1990). Noether’s theorem for local gauge transformations. American Journal of Physics, 58, 123131.Google Scholar
Kolmogorov, A. N. (1954). Preservation of conditionally periodic movements with small change in the Hamiltonian function. Doklady Akademii Nauk SSSR, 98, 527530 (in Russian). English translation in Appendix A of Dumas (2014).Google Scholar
Kolmogorov, A. N. (1957). The general theory of dynamical systems and classical mechanics. In Proceedings of the International Congress of Mathematicians 1954 (in Russian). Amsterdam: North-Holland. English translation in the Appendix of Abraham & Marsden (1978).Google Scholar
Konopinski, E. J. (1969). Classical Descriptions of Motion. San Francisco: W. H. Freeman.Google Scholar
Kot, M. (2014). A First Course in the Calculus of Variations. Providence, RI: American Mathematical Society.CrossRefGoogle Scholar
Kotkin, G. L. & Serbo, V. G. (1971). Collection of Problems in Classical Mechanics. Oxford: Pergamon Press.Google Scholar
Kozlov, V. V. (1983). Integrability and non-integrability in Hamiltonian mechanics. Russian Mathematical Surveys, 38, 176.Google Scholar
Lagrange, J. L. (1888). Mécanique Analytique. Vol. XI of Oeuvres Complètes. http://sites.mathdoc.fr/OEUVRES/.Google Scholar
Lam, K. S. (2014). Fundamental Principles of Classical Mechanics: A Geometrical Perspective. New Jersey: World Scientific.Google Scholar
Lanczos, C. (1970). The Variational Principles of Mechanics. New York: Dover.Google Scholar
Landau, L. D. & Lifshitz, E. (1976). Mechanics, 3rd edn. Oxford: Butterworth-Heinemann.Google Scholar
Laplace, P. S. (1840). Essai Philosophique sur les Probabilités. Paris: Bachelier. https://archive.org/stream/essaiphilosophiq00lapluoft#page/n5/mode/2up.Google Scholar
Laskar, J. (2013). Is the Solar System stable? Progress in Mathematical Physics, 66, 239270.CrossRefGoogle Scholar
Lawden, D. F. (1989). Elliptic Functions and Applications. New York: Springer.CrossRefGoogle Scholar
Lee, T. D. (1981). Particle Physics and Introduction to Field Theory. New York: Harwood Academic Publishers.Google Scholar
Lemos, N. A. (1979). Canonical approach to the damped harmonic oscillator. American Journal of Physics, 47, 857858.Google Scholar
Lemos, N. A. (1991). Remark on Rayleigh’s dissipation function. American Journal of Physics, 59, 660661.Google Scholar
Lemos, N. A. (1993). Symmetries, Noether’s theorem and inequivalent Lagrangians applied to nonconservative systems. Revista Mexicana de Física, 39, 304313.Google Scholar
Lemos, N. A. (1996). Singularities in a scalar field quantum cosmology. Physical Review D, 53, 42754279.Google Scholar
Lemos, N. A. (2000a). Short proof of Jacobi’s identity for Poisson brackets. American Journal of Physics, 68, 88.Google Scholar
Lemos, N. A. (2000b). Uniqueness of the angular velocity of a rigid body: Correction of two faulty proofs. American Journal of Physics, 68, 668669.CrossRefGoogle Scholar
Lemos, N. A. (2003). Sutilezas dos vínculos não-holônomos. Revista Brasileira de Ensino de Física, 25, 2834.Google Scholar
Lemos, N. A. (2005). Formulação geométrica do princípio de d’Alembert. Revista Brasileira de Ensino de Física, 27, 483485.Google Scholar
Lemos, N. A. (2014a). On what does not expand in an expanding universe: A very simple model. Brazilian Journal of Physics, 44, 9194.Google Scholar
Lemos, N. A. (2014b). Comment on “Unintended consequences of imprecise notation: An example from mechanics”, [Am. J. Phys. 81, 313–315 (2013)]. American Journal of Physics, 82, 164165.CrossRefGoogle Scholar
Lemos, N. A. (2014c). Incompleteness of the Hamilton-Jacobi theory. American Journal of Physics, 82, 848852.CrossRefGoogle Scholar
Lemos, N. A. (2015). Vínculos dependentes de velocidades e condição de integrabilidade de Frobenius. Revista Brasileira de Ensino de Física, 37, 4307–1–8.Google Scholar
Lemos, N. A. (2017a). Oscilador quártico e funções elípticas de Jacobi. Revista Brasileira de Ensino de Física, 39, e1305–1–8.Google Scholar
Lemos, N. A. (2017b). Atwood’s machine with a massive string. European Journal of Physics, 38, 065001.Google Scholar
Lemos, N. A. & Natividade, C. P. (1987). Harmonic oscillator in expanding universes. Nuovo Cimento B, 99, 211225.Google Scholar
Leubner, C. (1979). Coordinate-free rotation operator. American Journal of Physics, 47, 727729.Google Scholar
Lewis, H. R. Jr. & Riesenfeld, W. B. (1969). An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field. Journal of Mathematical Physics, 10, 14581473.Google Scholar
Lissauer, J. L. (1999). Chaotic motion in the Solar System. Reviews of Modern Physics, 71, 835845.Google Scholar
Lorentz, H. A., Einstein, A., Minkowski, H. & Weyl, H. (1952). The Principle of Relativity. New York: Dover.Google Scholar
Lutzky, J. L. (1978). Symmetry groups and conserved quantities for the harmonic oscillator. Journal of Physics A: Mathematical and General, 11, 249258.Google Scholar
Mann, R. A. (1974). The Classical Dynamics of Particles. New York: Academic Press.Google Scholar
Marion, J. B. & Heald, M. A. (1980). Classical Electromagnetic Radiation, 2nd edn. New York: Academic Press.Google Scholar
Marion, J. B. & Thornton, S. T. (1995). Classical Dynamics of Particles and Systems, 4th edn. Fort Worth: Saunders College Publishing.Google Scholar
Markus, L. & Meyer, K. R. (1974). Generic Hamiltonian dynamical systems are neither integrable nor ergodic. Memoirs of the American Mathematical Society, no. 144. Providence, RI: American Mathematical Society.Google Scholar
Marsden, J. E. & Ratiu, T. S. (1999). Introduction to Mechanics and Symmetry, 2nd edn. New York: Springer.Google Scholar
Marsden, J. E., O’Reilly, O. M., Wicklin, F. J. & Zombro, B. W. (1991). Symmetry, stability, geometric phases, and mechanical integrators (Part I). Nonlinear Sciences Today 1(1), 421; Symmetry, stability, geometric phases, and mechanical integrators (Part II). Nonlinear Sciences Today 1(2), 14–21.Google Scholar
Mathews, P. M. & Lakshmanan, M. (1974). On a unique non-linear oscillator. Quarterly of Applied Mathematics, 32, 215218.Google Scholar
Maxwell, J. C. (1891). A Treatise on Electricity and Magnetism, 3rd edn. 2 vols. New York: Dover (1954 reprint).Google Scholar
Mehra, J. (1994). The Beat of a Different Drum. Oxford: Oxford University Press.Google Scholar
Montgomery, R. (1991). How much does a rigid body rotate? A Berry’s phase from the 18th century. American Journal of Physics, 59, 394398.Google Scholar
Morales-Ruiz, J. J. & Ramis, J. P. (2001). A note on the non-integrability of some Hamiltonian systems with a homogeneous potential. Methods and Applications of Analysis, 8, 113120.Google Scholar
Moriconi, M. (2017). Condition for minimal harmonic oscillator action. American Journal of Physics, 85, 633634.Google Scholar
Moser, J. (1962). On invariant curves of area-preserving mappings of an annulus. Nachrichten von der Akademie der Wissenschaften in Göttingen, Mathematisch-Physikalische Klasse II, 1–20.Google Scholar
Moser, J. (1967). Convergent series expansions for quasi-periodic motions. Mathematische Annalen, 169, 136176.Google Scholar
Moser, J. (1973). Stable and Random Motions in Dynamical Systems. Princeton, NJ: Princeton University Press.Google Scholar
Nakagawa, K. & Yoshida, H. (2001). A necessary condition for the integrability of homogeneous Hamiltonian systems with two degrees of freedom. Journal of Physics A: Mathematical and General, 34, 21372148.Google Scholar
Nakane, M. & Fraser, C. G. (2002). The early history of Hamilton-Jacobi dynamics 1834– 1837. Centaurus, 44, 161227.Google Scholar
Neĭmark, J. I. & Fufaev, N. A. (1972). Dynamics of Nonholonomic Systems. Providence, RI: American Mathematical Society.Google Scholar
Nekhoroshev, N. N. (1977). An exponential estimate of the time of stability of nearly-integrable Hamiltonian systems. Russian Mathematical Surveys, 32(6), 165.Google Scholar
Noether, E. (1918). Invariante Variationsprobleme. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 2, 235257. English translation by M. A. Tavel: arXiv:physics/0503066.Google Scholar
Núñes-Yepes, H. N., Delgado, J. & Salas-Brito, A. L. (2001). Variational equations of Lagrangian systems and Hamilton’s principle. arXiv:math-ph/0107006.Google Scholar
Ohanian, H. C. (1976). Gravitation and Spacetime. NewYork: W. W. Norton & Company.Google Scholar
Ott, E. (1993). Chaos in Dynamical Systems. Cambridge: Cambridge University Press.Google Scholar
Pais, A. (1982) Subtle is the Lord … The Science and the Life of Albert Einstein. Oxford: Oxford University Press.Google Scholar
Pars, L. (1965). A Treatise on Analytical Dynamics. Woodbridge, CT: Ox Bow Press.Google Scholar
Pathria, R. K. (1972). Statistical Mechanics. Oxford: Pergamon Press.Google Scholar
Pauli, W. (1958). Theory of Relativity. New York: Dover.Google Scholar
Pearlman, N. (1967). Vector representation of rigid body rotation. American Journal of Physics, 35, 1164.Google Scholar
Peterson, I. (1993). Newton’s Clock: Chaos in the Solar System. NewYork: W. H. Freeman.Google Scholar
Protter, M. H. & Morrey, C. B. Jr. (1985). Intermediate Calculus. New York: Springer.Google Scholar
Pullen, R. A. & Edmonds, A. R. (1981). Comparison of classical and quantum spectra for a totally bound potential. Journal of Physics A: Mathematical and General, 14, L477– L484.Google Scholar
Reid, C. (1986). Hilbert-Courant. New York: Springer.Google Scholar
Rindler, W. (1982). Introduction to Special Relativity. Oxford: Clarendon Press.Google Scholar
Romer, R. H. (1978). Demonstration of the intermediate-axis theorem. American Journal of Physics, 46, 575576.Google Scholar
Rosen, G. (1969). Formulations of Classical and Quantum Dynamical Theory. NewYork: Academic Press.Google Scholar
Rund, H. (1966). The Hamilton-Jacobi Theory in the Calculus of Variations. London: D. Van Nostrand.Google Scholar
Russell, J. S. (1844). Report on Waves. 14th Meeting of the British Association for the Advancement of Science, 311–390.Google Scholar
Saari, D. G. (1990). A visit to the Newtonian N-body problem via elementary complex variables. American Mathematical Monthly, 97, 105119.Google Scholar
Saletan, E. J. & Cromer, A. H. (1970). A variational principle for nonholonomic systems. American Journal of Physics, 38, 892897.Google Scholar
Saletan, E. J. & Cromer, A. H. (1971). Theoretical Mechanics. New York: Wiley.Google Scholar
Scheck, F. (1994). Mechanics – From Newton’s Laws to Deterministic Chaos. Berlin: Springer.Google Scholar
Schiff, L. I. (1968). Quantum Mechanics, 3rd edn. New York: McGraw-Hill.Google Scholar
Schrödinger, E. (1982). Collected Papers on Wave Mechanics. New York: Chelsea Publishing Company.Google Scholar
Schwartz, L. (2008). Mathematics for the Physical Sciences. New York: Dover.Google Scholar
Sharan, P. (1982). Two theorems in classical mechanics. American Journal of Physics, 50, 351354.Google Scholar
Shinbrot, T., Grebogi, G., Wisdom, J. & Yorke, J. A. (1992). Chaos in a double pendulum. American Journal of Physics, 60, 491499.Google Scholar
Siegel, C. L. & Moser, J. (1971) Lectures on Celestial Mechanics. Berlin: Springer.Google Scholar
Sivardière, J. (1983). A simple mechanical model exhibiting a spontaneous symmetry breaking. American Journal of Physics, 51, 10161018.Google Scholar
Sivardière, J. (1986). Using the virial theorem. American Journal of Physics, 54, 11001103.Google Scholar
Sommerfeld, A. (1952). Mechanics. New York: Academic Press.Google Scholar
Soper, D. E. (1976). Classical Field Theory. New York: Wiley.Google Scholar
Spiegel, M. R. (1963). Advanced Calculus. New York: McGraw-Hill.Google Scholar
Spivak, M. (1965). Calculus on Manifolds. Menlo Park, CA: Benjamin.Google Scholar
Spivak, M. (1994). Calculus, 3rd edn. Houston, TX: Publish or Perish.Google Scholar
Stadler, W. (1982). Inadequacy of the usual Newtonian formulation for certain problems in particle mechanics. American Journal of Physics, 50, 595598.Google Scholar
Sternberg, S. (1994). Group Theory and Physics. Cambridge: Cambridge University Press.Google Scholar
Stillwell, J. (2010). Mathematics and Its History, 3rd edn. New York: Springer.Google Scholar
Störmer, C. (1907). Sur les trajectoires des corpuscules électrisés dans le espace sous l’action du magnétisme terrestre avec application aux aurores boréales. Archives des Sciences Physiques et Naturelles, 24, 518, 113–158, 221–247, 317–364. www.biodiversitylibrary.org/item/93687#page/5/mode/1up.Google Scholar
Sudarshan, E. C. G. & Mukunda, N. (1983). Classical Dynamics: A Modern Perspective. Malabar, FL: Robert E. Krieger.Google Scholar
Sundermeyer, K. (1982). Constrained Dynamics. New York: Springer.Google Scholar
Sussman, G. J. & Wisdom, J. with Mayer, M. E. (2001). Structure and Interpretation of Classical Mechanics. Cambridge, MA: MIT Press.Google Scholar
Symon, K. R. (1971). Mechanics, 3rd edn. Reading, MA: Addison-Wesley.Google Scholar
Synge, J. L. & Griffith, B. A. (1959). Principles of Mechanics, 3rd edn. New York: McGraw-Hill.Google Scholar
Tabor, M. (1989). Chaos and Integrability in Nonlinear Dynamics. New York: Wiley.Google Scholar
Taylor, J. R. (2005). Classical Mechanics. Mill Valley, CA: University Science Books.Google Scholar
Terra, M. S., Souza, R. M., and Farina, C. (2016). Is the tautochrone curve unique? American Journal of Physics, 84, 917923.Google Scholar
Thirring, W. (1997). Classical Mathematical Physics. Berlin: Springer.Google Scholar
Tiersten, M. S. (1991). Moments not to forget – The conditions for equating torque and rate of change of angular momentum around the instantaneous center. American Journal of Physics, 59, 733738.Google Scholar
Tiersten, M. S. (1992). Erratum. American Journal of Physics, 60, 187.Google Scholar
Tufillaro, N. (1986). Integrable motion of a swinging Atwood’s machine. American Journal of Physics, 54, 142143.Google Scholar
Tufillaro, N. B., Abbott, T. A. & Griffiths, D. J. (1984). Swinging Atwood’s machine. American Journal of Physics, 52, 895903.Google Scholar
Tung, W. (1985). Group Theory in Physics. Singapore: World Scientific.Google Scholar
Van Dam, N. & Wigner, E. (1966). Instantaneous and asymptotic conservation laws for classical relativistic mechanics of interacting point particles. Physical Review, 142, 838843.Google Scholar
van der Waerden, B. L. (ed.) (1967). Sources of Quantum Mechanics. New York: Dover.Google Scholar
van Kampen, N. G. & Lodder, J. J. (1984). Constraints. American Journal of Physics, 52, 419424.Google Scholar
Weinstock, R. (1961). Laws of classical motion: What’s F? What’s m? What’s a? American Journal of Physics, 29, 698702.Google Scholar
Weinstock, R. (1974). Calculus of Variations. New York: Dover.Google Scholar
Westfall, R. (1983). Never at Rest: A Biography of Isaac Newton. Cambridge: Cambridge University Press.Google Scholar
Whittaker, E. T. (1944). A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. New York: Dover.Google Scholar
Whittaker, E. T. (1951). A History of the Theories of Aether and Electricity, Vol. I: The Classical Theories. London: Thomas Nelson and Sons.Google Scholar
Whittaker, E. T. & Watson, G. N. (1927). A Course of Modern Analysis. Cambridge: Cambridge University Press.Google Scholar
Wiggins, S. (2003). Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. New York: Springer.Google Scholar
Wisdom, J. (1987). Chaotic behaviour in the Solar System. Proceedings of the Royal Society of London. Series A, Mathematical and Physical, 413, 109129.Google Scholar
Yandell, B. H. (2002). The Honors Class: Hilbert’s Problems and Their Solvers. Natick, MA: A K Peters.Google Scholar
Yoshida, H. (1987). A criterion for the nonexistence of an additional integral in Hamiltonian systems with a homogeneous potential. Physica D, 29, 128142.Google Scholar
Yoshida, H. (1989). A criterion for the non-existence of an additional analytic integral in Hamiltonian systems with n degrees of freedom. Physics Letters A, 141, 108112.Google Scholar
Yourgrau, W. & Mandelstam, S. (1968). Variational Principles in Dynamics and Quantum Theory. New York: Dover.Google Scholar
Zia, R. K. P., Redish, E. F. & McKay, S. R. (2009). Making sense of the Legendre transform. American Journal of Physics, 77, 614622.Google Scholar
Ziglin, S. L. (1983). Branching of solutions and nonexistence of first integrals in Hamiltonian mechanics I. Journal of Functional Analysis and Applications, 16, 181189; Branching of solutions and nonexistence of first integrals in Hamiltonian mechanics II. Journal of Functional Analysis and Applications, 17, 6–17.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×