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1: William P. Reinhardt
This is closely connected with his interests in classical dynamical “chaos,” an area where he coauthored a book, Chaos in atomic physics with Reinhold Blümel. …
2: 23.21 Physical Applications
§23.21 Physical Applications
§23.21(i) Classical Dynamics
In §22.19(ii) it is noted that Jacobian elliptic functions provide a natural basis of solutions for problems in Newtonian classical dynamics with quartic potentials in canonical form ( 1 - x 2 ) ( 1 - k 2 x 2 ) . …
3: 22.19 Physical Applications
§22.19(i) Classical Dynamics: The Pendulum
§22.19(ii) Classical Dynamics: The Quartic Oscillator
§22.19(v) Other Applications
Numerous other physical or engineering applications involving Jacobian elliptic functions, and their inverses, to problems of classical dynamics, electrostatics, and hydrodynamics appear in Bowman (1953, Chapters VII and VIII) and Lawden (1989, Chapter 5). …
4: 18.39 Physical Applications
§18.39 Physical Applications
§18.39(i) Quantum Mechanics
§18.39(ii) Other Applications
For applications of Legendre polynomials in fluid dynamics to study the flow around the outside of a puff of hot gas rising through the air, see Paterson (1983). …
5: 32.16 Physical Applications
§32.16 Physical Applications
Statistical physics, especially classical and quantum spin models, has proved to be a major area for research problems in the modern theory of Painlevé transcendents. …
Integrable Continuous Dynamical Systems
6: 9.16 Physical Applications
Airy functions are applied in many branches of both classical and quantum physics. … The frequent appearances of the Airy functions in both classical and quantum physics is associated with wave equations with turning points, for which asymptotic (WKBJ) solutions are exponential on one side and oscillatory on the other. …Within classical physics, they appear prominently in physical optics, electromagnetism, radiative transfer, fluid mechanics, and nonlinear wave propagation. … In fluid dynamics, Airy functions enter several topics. … The KdV equation and solitons have applications in many branches of physics, including plasma physics lattice dynamics, and quantum mechanics. …
7: Bibliography
  • J. V. Armitage (1989) The Riemann Hypothesis and the Hamiltonian of a Quantum Mechanical System. In Number Theory and Dynamical Systems (York, 1987), M. M. Dodson and J. A. G. Vickers (Eds.), London Math. Soc. Lecture Note Ser., Vol. 134, pp. 153–172.
  • V. I. Arnol d (1997) Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics, Vol. 60, Springer-Verlag, New York.
  • U. M. Ascher, R. M. M. Mattheij, and R. D. Russell (1995) Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. Classics in Applied Mathematics, Vol. 13, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
  • 8: Bibliography B
  • L. E. Ballentine and S. M. McRae (1998) Moment equations for probability distributions in classical and quantum mechanics. Phys. Rev. A 58 (3), pp. 1799–1809.
  • R. W. Barnard, K. Pearce, and K. C. Richards (2000) A monotonicity property involving F 2 3 and comparisons of the classical approximations of elliptical arc length. SIAM J. Math. Anal. 32 (2), pp. 403–419.
  • R. Becker and F. Sauter (1964) Electromagnetic Fields and Interactions. Vol. I, Blaisdell, New York.
  • E. D. Belokolos, A. I. Bobenko, V. Z. Enol’skii, A. R. Its, and V. B. Matveev (1994) Algebro-geometric Approach to Nonlinear Integrable Problems. Springer Series in Nonlinear Dynamics, Springer-Verlag, Berlin.
  • 9: Bibliography D
  • B. Deconinck and H. Segur (2000) Pole dynamics for elliptic solutions of the Korteweg-de Vries equation. Math. Phys. Anal. Geom. 3 (1), pp. 49–74.
  • R. L. Devaney (1986) An Introduction to Chaotic Dynamical Systems. The Benjamin/Cummings Publishing Co. Inc., Menlo Park, CA.
  • D. K. Dimitrov and G. P. Nikolov (2010) Sharp bounds for the extreme zeros of classical orthogonal polynomials. J. Approx. Theory 162 (10), pp. 1793–1804.
  • K. Driver and K. Jordaan (2013) Inequalities for extreme zeros of some classical orthogonal and q -orthogonal polynomials. Math. Model. Nat. Phenom. 8 (1), pp. 48–59.
  • 10: Bibliography W
  • A. Weil (1999) Elliptic Functions According to Eisenstein and Kronecker. Classics in Mathematics, Springer-Verlag, Berlin.
  • E. T. Whittaker (1964) A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. 4th edition, Cambridge University Press, Cambridge.